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arXiv · 2010.15613

Uniqueness and energy balance for isentropic Euler equation with stochastic forcing

Shyam Sundar Ghoshal·Animesh Jana·Barun Sarkar
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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 Hölder regularity $C^α,α>1/2$ 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 Hölder regularity $C^α,α>1/3$. Both the results have been obtained in a more general setting by considering regularity in Besov space.

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Shyam Sundar Ghoshal, Animesh Jana, Barun Sarkar. 2020-10-29. Uniqueness and energy balance for isentropic Euler equation with stochastic forcing. https://arxiv.org/abs/2010.15613

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