English

Uniqueness and energy balance for isentropic Euler equation with stochastic forcing

Analysis of PDEs 2020-10-30 v1 Probability

Abstract

In this article, we prove uniqueness and energy balance for isentropic Euler system driven by a cylindrical Wiener process. Pathwise uniqueness result is obtained for weak solutions having H\"older regularity Cα,α>1/2C^{\alpha},\alpha>1/2 in space and satisfying one-sided Lipschitz bound on velocity. We prove Onsager's conjecture for isentropic Euler system with stochastic forcing, that is, energy balance equation for solutions enjoying H\"older regularity Cα,α>1/3C^{\alpha},\alpha>1/3. Both the results have been obtained in a more general setting by considering regularity in Besov space.

Keywords

Cite

@article{arxiv.2010.15613,
  title  = {Uniqueness and energy balance for isentropic Euler equation with stochastic forcing},
  author = {Shyam Sundar Ghoshal and Animesh Jana and Barun Sarkar},
  journal= {arXiv preprint arXiv:2010.15613},
  year   = {2020}
}