Publications

W. Varnhorn: Second order semi-discretization for unsteady Stokes flow. In: Proc. Topical Problems of Fluid Mechanics 2024, Inst. Thermomech. & Czech Acad. Sci. Prague (2024) 240-247

W. Varnhorn: An approximation method for non-stationary Stokes flow. In: Proc. Topical Problems of Fluid Mechanics 2023, Inst. Thermomech. & Czech Acad. Sci. Prague (2023) 202-209

W. Varnhorn: On the Poisson equation in exterior domains. Constructive Mathematical Analysis 5 no. 3 (2022) 134-140

S. Mfogo, W. Varnhorn: Numerical solutions for the Newton and Stokes potentials using approximate approximations. Journal of Computational Mathematica 6 no.1 (2022) 159-199

W. Varnhorn: Maximum modulus estimates for the linear steady Stokes equations in domains of Rn⁽ n ≥ 2). In: Proc. Topical Problems of Fluid Mechanics 2022, Inst. Thermomech. & Czech Acad. Sci. Prague (2022) 190-193

W. Varnhorn: A Lagrangian approach for weak solutions of the Navier-Stokes equations. In: Proc. Topical Problems of Fluid Mechanics 2020, Inst. Thermomech. & Czech Acad. Sci. Prague (2020) 249-255

W. Varnhorn: On a stabilized Navier-Stokes system. In: Proc. Topical Problems of Fluid Mechanics 2019, Inst. Thermomech. & Czech Acad. Sci. Prague (2019) 205-214

W. Varnhorn: Steady and unsteady Navier-Stokes flow with Lagrangian differences. In: Differential and Difference Equations with Applications. Springer Proc. Math. Stat. 230 (2018) 559-568

W. Varnhorn: On the motion of viscous incompressible flow: The Navier-Stokes equations. In: Proc. Topical Problems of Fluid Mechanics 2018, Inst. Thermomech. & Czech Acad. Sci. Prague (2018) 315-324

W. Varnhorn: Approximate approximations for 3-D Stokes flow. In: Proc. Topical Problems of Fluid Mechanics 2017, Inst. Thermomech. & Czech Acad. Sci. Prague (2017) 313-320

W. Varnhorn: A Crank-Nicholson method for non-stationary Stokes flow. In: Proc. Topical Problems of Fluid Mechanics 2016, Inst. Thermomech. & Czech Acad. Sci. Prague (2016) 237-240

W. Varnhorn, F. Zanger: A remark on the fractional step theta scheme for the nonstationary Stokes equations. In: Differential and Difference Equations with Applications, Springer Proc. Math. Stat. 164 (2016) 443-451

D. Medkova, M. Ptashnyk, W. Varnhorn: Generalized Darcy-Oseen resolvent problem. Math. meth. Appl. Sci. 39 (2016) 1621-1630

R. Farwig, C. Simader, H. Sohr, W. Varnhorn: General properties of the Helmholtz decomposition in spaces of Lq-type. Contemp. Math. 666 (2016) 163-177

M. Abdulhameed, I. Hashim, R. Roslan, W. Varnhorn: The unsteady flow of a third-grade fluid caused by the periodic motion of an infinite wall with transpiration. Alexandria Engineering J. 54 (2015) 1233-1241

R. Farwig, H. Sohr, W. Varnhorn: Local strong solutions of the nonhomogeneous Navier-Stokes system with control of the interval of existence. Topol. Meth. Nonl. Anal. 46 no. 2 (2015) 999-1012

N. Asanalieva, C. Heutling, W. Varnhorn: Time delay and Lagrangian approximation for Navier-Stokes flow. Analysis 35 no. 4 (2015) 213-229

D. Medkova, M. Ptashnyk, W. Varnhorn: Integral representation of a solution to the Stokes-Darcy problem, Math. Meth. Appl. Sci. 38 no. 17 (2015) 3968-3979

W. Varnhorn: Time delay and Lagrangian differences for viscous incompressible fluid flow. In: Proc. Topical Problems of Fluid Mechanics 2015, Inst. Thermomech. & Czech Acad. Sci. Prague (2015) 255-260

W. Varnhorn: The Stokes resolvent equations in 2d exterior domains. P. A. M. M. 14 (2014) 741-742

N. Asanalieva, C. Heutling, W. Varnhorn: The Navier-Stokes equations with particle methods. P. A. M. M. 14 (2014), 739-740

C. Heutling, W. Varnhorn: A first order method for non-steady Stokes flow. In: Proc. Coll. Fluid Dynamics 2014, Inst. Thermomech. & Czech Acad. Sci. Prague (2014) 17-18

R. Farwig, H. Sohr, W. Varnhorn: Besov space regularity conditions for weak solutions of the Navier-Stokes equations. J. Math. Fluid Mech. 16 (2014) 307-320

C. Simader, H. Sohr, W. Varnhorn: Necessary and sufficient conditions for the existence of Helmholtz decompositions in general domains. Annali dell'Università di Ferrara 60 no. 1 (2014) 245-262

S. Kračmar, D. Medková, Š. Nečasová, W. Varnhorn: A maximum modulus theorem for the Oseen problem. Annali di Mat. Pura Applic. 192 no. 6 (2013) 1059-1076

F. Zanger, W. Varnhorn: On approximation and computation of Navier-Stokes flow. J. Part. Diff. Eq. 26 no. 2 (2013) 151-171

D. Medková, E. Skopin, W. Varnhorn: The Robin problem for the scalar Oseen equation. Math. meth. Appl. Sci. 36 (2013) 2237-2242

W. Varnhorn: Maximum modulus estimates for the linear steady Stokes system, P. A. M. M. 12 (2012) 589-590

W. Varnhorn: Time delay and material differences for non-stationary Navier-Stokes flow. Far East J. Appl. Math. 72 no. 1 (2012) 49-59

D. Medková, E. Skopin, W. Varnhorn: The boundary value problems for the scalar Oseen equation. Math. no. 285 no. 17-18 (2012) 2208-2221

R. Farwig, H. Sohr, W. Varnhorn: Extensions of Serrin's uniqueness and regularity conditions for the Navier-Stokes equations, J. Math. Fluid Mech. 14 (2012) 529-540

F. Müller, W. Varnhorn: Constructing approximate solutions for three-dimensional stationary Stokes flow, Dyn. Sys. Diff. Equa. Supplement (2011) 1091-1100

W. Varnhorn: A maximum modulus estimate for the Stokes equations. In: Proc. Coll. Fluid Dynamics 2011, Inst. Thermomech. & Czech Acad. Sci. Prague (2011) 49-50

D. Medková, W. Varnhorn: The planar Dirichlet problem for the Stokes equations, Math. Meth. Appl. Sci 34 (2011) 1097-1109

F. Müller, W. Varnhorn: On approximation and numerical solution of Fredholm integral equations of second kind using quasi-interpolation. Appl. Math. comp. 217 (2011) 6409-6416

F. Zanger, W. Varnhorn: Semidiscretization of nonstationary linear Stokes flow. In: Proc. Conf. Topical Problems of Fluid Mechanics 2011, Inst. Thermomech. & Czech Acad. Sci. Prague (2011) 133-136

N. Asanalieva, W. Varnhorn: Non-steady Navier-Stokes flow with steady Lagrangian differences. In: Proc. Conf. Topical Problems of Fluid Mechanics 2011, Inst. Thermomech. & Czech Acad. Sci. Prague (2011) 1-4

R. Farwig, H. Sohr, W. Varnhorn: Necessary and sufficient conditions on local strong solvability of the Navier-Stokes system. Applic. Anal 90 no. 1 (2011) 47-58

Š. Nečasová, R. Rautmann, R. Temam, W. Varnhorn: Special Issue in honor of Prof. Solonnikov's 75th birthday: Preface. Applic. Anal 90 no. 1 (2011) 1-3

Werner Varnhorn: Non-Steady Stokes flow and finite differences. In: Proc. Coll. Fluid Dynamics 2010, Inst. Thermomech. & Czech Acad. Sci. Prague (2010) 31-32

P. Deuring, W. Varnhorn: On Oseen Resolvent Estimates. Diff. Int. equa. 23 no. 11-12 (2010) 1139-1149

D. Medková, W. Varnhorn: The Dirichlet problem for the Stokes system and the integral equations' method. Int. J. Pure Appl. Math. 62 (2010) 49-55

Š. Nečasová, R. Rautmann, W. Varnhorn: Special Issue in honor of Prof. Solonnikov's 75th birthday: Preface. Discr. Contin. Dyn. Syst. Ser. S 3 no. 2 (2010) i-ii

W. Varnhorn: A numerical method for non-stationary Stokes Flow. In: Advances in Mathematical Fluid Mechanics, R. Rannacher & A. Sequeira (eds.), Springer-Verlag (2010) 589-611

N. Asanalieva, W. Varnhorn: The Navier-Stokes equations with regularization. P. A. M. M. 9 (2009) 545-546

F. Müller, W. Varnhorn: Approximate solutions and error estimates for a Stokes boundary value problem, Annali dell'Università di Ferrara 55 (2009) 309-323

N. Asanalieva, W. Varnhorn: The Navier-Stokes equations with material differences. In: Proc. Coll. Fluid Dynamics 2009, Inst. Thermomech. & Czech Acad. Sci. Prague (2009) 1-2

R. Farwig, H. Sohr, W. Varnhorn: On optimal initial value conditions for local strong solutions of the Navier-Stokes equations. Ann. Univ. Ferrara 55 (2009) 89-110

D. Medková, W. Varnhorn: The Stokes equations in exterior n-dimensional domains. Int. J. Pure Appl. Math. 50 (2009) 175-180

W. Varnhorn: The non-homogeneous Stokes system in exterior domains. P. A. M. M. 8 (2008) 10757-10758

W. Varnhorn: Approximate approximations and the Poisson equation in the whole space. Int. J. Pure Appl. Math. 49 (2008) 539-545

D. Medková, W. Varnhorn: Boundary value problems for the Stokes equations with jumps in open sets. Applic. Anal. 87 (2008) 829-849

W. Varnhorn: Lagrangian approximations and weak solutions of the Navier-Stokes equations. Banach Center Publications 81 (2008) 515-532

W. Varnhorn: On Lagrangian approximation for the Navier-Stokes system. Int. J. Pure Appl. Math. 42 (2008) 191-196

W. Varnhorn: The Navier-Stokes equations with time delay. Appl. Math. Sci. 2 no. 20 (2008) 947-960

T. Samrowski, W. Varnhorn: Approximate approximations for the Poisson and the Stokes equations. Appl. Math. Sci. 2 no. 19 (2008) 929-946

W. Varnhorn: Time delay and material differences for viscous incompressible fluid flow. In: WSPC - Proc. Equadiff Conf. Vienna Univ. Technol. (2007) 1-6

W. Varnhorn: Boundary integral equations and maximum modulus estimates for the Stokes system. P. A. M. M. 7 (2007) 1042603 - 1042604

W. Varnhorn: The Navier-Stokes equations with particle methods. In: Topics on Partial Differential Equations, Jindrich Nečas Center for Mathematical Modeling, Lecture Notes 2, Kaplicky & Nečasová (Eds.), Charles U Prague (2007) 121-157

S. König, W. Varnhorn: Approximate approximations and a boundary point method for the linearized Stokes system. Int. J. Pure Appl. Math. 37 (2007) 441-451

F. Müller, W. Varnhorn: Error estimates for approximate approximations with Gaussian kernels on compact intervals. J. Approx. T. 145 (2007) 171-181

S. König, W. Varnhorn: The Stokes equations: A numerical approach for the boundary value problem. In: Proc. Conf. Topical Problems of Fluid Mechanics 2007, Inst. Thermomech. & Czech Acad. Sci. Prague (2007) 91-94

W. Varnhorn: The Stokes equations: A numerical approach for the whole space problem. In: Proc. Conf. Topical Problems of Fluid Mechanics 2007, Inst. Thermomech. & Czech Acad. Sci. Prague (2007) 193-196

W. Varnhorn: A Lagrangian approach to the nonlinear Navier-Stokes equations. WSEAS Transactions on Math. 3 no. 5 (2006) 265-273

W. Varnhorn: The Navier-Stokes equations with Lagrangian differences. In: Proc. WSEAS/IASME Int. Conf. Contin. Mech. Evia Island Greece (2006) 175-179

F. Müller, W. Varnhorn: An approximation method using approximate approximations. Applic. Anal. 85 (2006) 669-680

W. Varnhorn: An energy conserving Lagrangian approximation for the stationary nonlinear Navier-Stokes equations. P. A. M. M. 5 (2005) 635-636

F. Müller, W. Varnhorn: On approximate approximations of potentials. P. A. M. M. 4 (2004) 710-711

W. Varnhorn: Numerical methods for the Navier-Stokes equations. In: Proc. Coll. Fluid Dynamics 2004, Inst. Thermomech. & Czech Acad. Sci. Prague (2004) 207-210

T. Samrowski, W. Varnhorn: The Poisson equation in homogeneous Sobolev spaces. Int. J. Math. and Math. Sci. 36 (2004) 1909-1921

W. Varnhorn: The boundary value problems of the Stokes resolvent equations in n dimensions. Math. Nachr. 269-270 (2004) 210-230

M. Peter, W. Varnhorn: Maximum value estimates for the Stokes equations. P. A. M. M. 1 (2002) 416-417

M. Peter, W. Varnhorn: The maximum modulus theorem for the Stokes system. In: Proc. Int. Sem. Euler and Navier-Stokes equations 2001, Inst. Thermomech. & Czech Acad. Sci. Prague (2001) 109-112

W. Varnhorn: Boundary value problems and integral equations for the Stokes resolvent in bounded and exterior domains of ^Rn. In: Theory of the Navier-Stokes Equations, Heywood et al. (eds.), World Scientific Publishing (1998) 206-224

W. Varnhorn: Boundary integral equations for the Stokes problem in exterior domains of ^Rn. In: Navier-Stokes Equations and Related Nonlinear Problems, Proc. Int. Conf. Madeira 1994, Sequeira (ed.), Plenum Press (1995) 117-127

W. Varnhorn: The boundary value problems for the Stokes resolvent equations in^R2. In: Inverse Scattering and Potential Problems in Mathematical Physics, Proc. Oberwolfach 1993, Kleinman, Kress, Martensen (eds.), Meth. u. Verf. d. Mathem. Phys. 40, Peter Lang (1995) 169-188

W. Varnhorn: On strong solutions of the Stokes equations in exterior domains. Acta Applic. Math. 37 (1994) 205-214

W. Varnhorn: The Stokes equations. Mathematical Research Volume 76, Akademie Verlag (1994) 1-154

W. Varnhorn: Solutions in Lebesgue spaces to the stationary Stokes equations in unbounded open sets of ^Rn. Adv. Math. Sci. Appl. 4 (1994) 191-208

W. Varnhorn: Finite differences and boundary element methods for nonstationary viscous incompressible flow. In: Numerical Analysis and Mathematical Modeling, Banach Center Publ. 29 (1994) 135-154

W. Borchers, W. Varnhorn: The Stokes resolvent in outer regions of^R2. Z. A. M. M. 73 (1993) T785-T788

O. Meister, W. Varnhorn: Spatial discretization using barycentric coordinates for partial differential equations in conservative form. Z. A. M. M. 73 (1993) T660-T663

W. Borchers, W. Varnhorn: On the boundedness of the Stokes semigroup in two-dimensional exterior domains. Math. Z. 213 (1993) 275-300

W. Varnhorn: On Eulerian and Lagrangian representation of steady incompressible fluid flow. Nonlin. Anal. 20 (1993) 993-1000

W. Varnhorn: A fractional step method for regularized Navier-Stokes equations. In: The Navier-Stokes Equations, Theory and Numerical Methods 2, Proc. Oberwolfach 1991, Heywood et al. (eds.). Springer Lect. N. Math. 1530 (1992) 196-209

W. Varnhorn: Stationary incompressible flow and the method of characteristics. Z. A. M. M. 72 (1992) T602-T604

W. Varnhorn: A particle method for the steady state Navier-Stokes equations. In: Proc. Int. Sem. Euler and Navier-Stokes equations 2, Inst. Thermomech. & Czech Acad. Sci. Prague (1992) 49-51

W. Varnhorn: Time delay and finite differences for the nonstationary nonlinear Navier-Stokes equations. Math. meth. Appl. Sci. 15 (1992) 89-108

P. Deuring, W. Varnhorn: Schauder estimates for the single layer potential in hydrodynamics. Math. Nachr. 157 (1992) 277-289

P. Deuring, W. Varnhorn: On strong solutions of Poisson's equation in Beppo Levi spaces. J. Appl. Math. Phys. (ZAMP) 43 (1992) 1023-1037

W. Varnhorn: Time stepping procedures for the nonstationary Stokes equations. Math. meth. Appl. Sci. 15 (1992) 39-55

W. Varnhorn: The Poisson equation with weights in exterior domains of ^Rn. Applic. Anal. 43 (1992) 135-145

W. Varnhorn: On the construction of a numerical solution of the initial boundary value problem for the nonlinear equations of Navier-Stokes. Analysis 11 (1991) 191-207

W. Varnhorn: An explicit potential theory for the Stokes resolvent boundary value problems in three dimensions. Manuscr. Math. 70 (1991) 339-361

W. Varnhorn: The Poisson equation in Beppo Levi spaces. Preprint 1319 TU Darmstadt (1990) 1-11

H. Sohr, W. Varnhorn: On decay properties of the Stokes equations in exterior domains. In: The Navier-Stokes Equations, Theory and Numerical Methods, Proc. Oberwolfach 1988, Heywood et al. (eds.), Springer Lect. N. Math. 1431 (1990) 134-151

W. Varnhorn: Efficient quadrature for a boundary element method to compute three-dimensional Stokes flow. Int. J. Num. Meth. Fluids 9 (1989) 185-191

W. Varnhorn: On the boundary element method for three-dimensional flows in the range of small and large Reynolds numbers. Z. A. M. M. 68 (1988) T482-T483

W. Varnhorn: Energy conserving Lagrangian approximation for the equations of Navier-Stokes. J. Diff. Equa. 76 no. 2 (1988) 256-268

W. Varnhorn: A new method for the numerical calculation of three-dimensional Navier-Stokes flows. Z. A.M. M. 67 (1987) T337-T339

R. Rautmann, W. Varnhorn: The Navier-Stokes initial boundary value problem with a difference approximation. Z. A. M. M. 65 (1985) T360-T362

F.-K. Hebeker, M. Specovius, W. Varnhorn: On the Hölder continuity of the direct values of the tangential derivatives of Stokes single layer potentials. Z. A. M. M. 64 (1984) T362-T364