A moment extension of Lions' method for SPDEs

Master thesis (2021)

Authors

J.P.C. Hoogendijk Electrical Engineering, Mathematics and Computer Science

Contributors

M.C. Veraar Analysis - EEMCS (mentor)
M.V. Gnann Analysis - EEMCS (mentor)
Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Copyright: © 2021 Jochem Hoogendijk
More Info
expand_more

Published Date

30-08-2021

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

This master's thesis introduces a new $p$-dependent coercivity condition through which $L^p(\Omega; L^2([0, T]; X))$ estimates can be obtained for a large class of SPDEs in the variational framework. Using these estimates, we obtain existence and uniqueness results by using a Galerkin approximation argument. The framework that is built is applied to many SPDEs such as stochastic heat equations with Dirichlet and Neumann boundary conditions, Burger's equation and Navier-Stokes in 2D. Furthermore, we obtain known results for systems of SPDEs and higher order SPDEs using our unifying coercivity condition. We also obtain first steps towards a theory of higher order regularity of stochastic heat equations.

Files

ThesisHoogendijkFINAL.pdf
(pdf | 1.28 Mb)
Unknown license