LOCAL AND GLOBAL EXISTENCE OF SMOOTH SOLUTIONS FOR THE STOCHASTIC EULER EQUATIONS WITH MULTIPLICATIVE NOISE

• 成果类型: Article
• 署名作者: Glatt-Holtz, Nathan E.; Vicol, Vlad C.
• 署名单位: Indiana University System; Indiana University Bloomington; University of Chicago
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/12-AOP773
• 发表日期: 2014
• 页码: 80-145
• 关键词: navier-stokes equations; partial-differential equations; pathwise solutions; martingale

摘要

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 suitable nonlinear multiplicative noise. In the two-dimensional case we obtain the global existence of these solutions with additive or linear-multiplicative noise. Finally, 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.