Uniqueness and energy balance for isentropic Euler equation with stochastic forcing
Nonlinear Analysis: Real World Applications
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.
Ghoshal, Shyam Sundar; Jana, Animesh; and Sarkar, Barun, "Uniqueness and energy balance for isentropic Euler equation with stochastic forcing" (2021). Journal Articles. 1781.
Open Access, Green