Galerkin approximation and the strong solution of theNavier-Stokes equation
By Hannelore Breckner. 2000
74 citations recorded by the source corpus.
We consider a stochastic equation of Navier-Stokes type containing a noise part given by a stochastic integral with respect to a Wiener process. The purpose of this paper is to approximate the solution of this nonlinear equation by the Galerkin method. We prove the convergence in mean square.
Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Finance
View Paper: https://www.semanticscholar.org/paper/dd3aef73863220f3748a8b72d3d28027799bb28e
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Citations in the corpus
- Local martingale and pathwise solutions for an abstract fluids model (2010, methodology): “red, from the PDE point of view, weak solutions evolving in time only in L2 x. More recently, pathwise solutions (both local and global in time) for a multiplicative noise have been investigated. See [5, 2, 6, 36]. None of these works addressed the existence and uniqueness of a local pathwise soluti”
- Parameter estimation for the stochastically perturbed Navier-Stokes equations (2010, unknown): “See, for instance, [2, 3, 4, 7, 12, 13, 30] and containing references.”
- Strong pathwise solutions of the stochastic Navier-Stokes system (2009, background): “In the two-dimensional setting, Da Prato and Zabczyk [12] and later Breckner [4] as well as Menaldi and Sritharan [21] established the existence of pathwise solutions where u takes values in L∞([0, T ], L2).”