Uniqueness and energy balance for isentropic Euler equation with stochastic forcing. (October 2021)

• Record Type: Journal Article
• Authors: Ghoshal, Shyam Sundar; Jana, Animesh; Sarkar, Barun
• Is Part Of: Nonlinear analysis. Volume 61(2021)
• Publication Date: 2021-10
• Subjects: Stochastic isentropic Euler system -- Pathwise weak solution -- Uniqueness -- Besov space -- Energy balance -- Onsager's conjecture; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103328
• Languages: English
• ISSNs: 1468-1218

Abstract

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.