Uniqueness and energy balance for isentropic Euler equation with stochastic forcing

• Published in: Nonlinear analysis: real world applications Vol. 61; p. 103328
• Main Authors: Ghoshal, Shyam Sundar, Jana, Animesh, Sarkar, Barun
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-10-2021
• Subjects: Besov space; Energy balance; Onsager’s conjecture; Pathwise weak solution; Stochastic isentropic Euler system; Uniqueness; Energy balance; Stochastic isentropic Euler system; Onsager’s conjecture; Pathwise weak solution; Besov space; Uniqueness
• ISSN: 1468-1218; 1878-5719
• DOI: 10.1016/j.nonrwa.2021.103328

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 Cα,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 Cα,α>1∕3. Both the results have been obtained in a more general setting by considering regularity in Besov space.