Local and global existence of smooth solutions for the stochastic Euler equations with multiplicative noise

2011/11/06 by Glatt-Holtz, Nathan E., Vicol, Vlad C. · 2 citations
#35Q35 #60H15 #76B03 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1111.1451

Abstract

We establish the local existence of pathwise solutions for the stochastic Euler equations in a three-dimensional bounded domain with slip boundary conditions and a very general nonlinear multiplicative noise. In the two-dimensional case we obtain the global existence of these solutions with additive or linear-multiplicative noise. Lastly, we show that, in the three dimensional case, the addition of linear multiplicative noise provides a regularizing effect; the global existence of solutions occurs with high probability if the initial data is sufficiently small, or if the noise coefficient is sufficiently large.

Cited by

• Local pathwise solutions and regularization by noises for the stochastic hyperbolic Keller-Segel equation
• Strong solution for polymeric fluid-structure interaction with small initial acceleration

Related

• On a 2D stochastic Euler equation of transport type: existence and geometric formulation
• Stochastic incompressible Euler equations in a two-dimensional domain
• On local well-posedness of the stochastic incompressible density-dependent Euler equations
• No blow-up by nonlinear Itô noise for the Euler equations
• Stationary solutions to stochastic 3D Euler equations in Hölder space