Uniqueness and energy balance for isentropic Euler equation with stochastic forcing. (October 2021) - Ghoshal, Shyam Sundar; Jana, Animesh; Sarkar, Barun
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.