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Uniqueness and energy balance for isentropic Euler equation with stochastic forcing. (English) Zbl 1477.35144

Summary: 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 \(C^\alpha\), \(\alpha > 1 / 2\) 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 Hölder regularity \(C^\alpha\), \(\alpha > 1 / 3\). Both the results have been obtained in a more general setting by considering regularity in Besov space.

MSC:

35Q31 Euler equations
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35D30 Weak solutions to PDEs
35B65 Smoothness and regularity of solutions to PDEs
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