Erik Heidrich (RPTU Kaiserslautern-Landau): Boundedness of the H∞-calculus for the Stokes operator in Lq-spaces with Muckenhoupt weights
Zoom-Link:
https://uni-kassel.zoom-x.de/j/66183030603?pwd=3TYcaqxJjpBNz1uvOXMUfdpH0Q42r7.1
Meeting-ID: 661 8303 0603
Kenncode: 341157
Abstract:
In the study of the incompressible Navier-Stokes equations one is interested in functional analytic properties of the Stokes operator, such as maximal regularity or a bounded H∞-calculus. In particular, the existence of a bounded H∞-calculus is a strong result that implies further properties such as a probabilistic analogue of maximal regularity called stochastic maximal regularity. This makes it possible to study the incompressible Navier-Stokes equations with an additional stochastic noise term in a functional analytic framework.
When one deals with solutions of low regularity, it can be advantageous to study the problem not in the usual Sobolev scale, but instead in spaces with weights, where the weights provide additional control over the behaviour of the solution near the boundary. In particular, it can be possible to simplify the set of boundary conditions accompanying the equation.
In this talk, we will prove the boundedness of the H∞-calculus for the Stokes operator in Lq-spaces with Muckenhoupt weights. Then, we provide an application to the incompressible Navier-Stokes equations with Dirichlet boundary conditions in three dimensions.