Onsager's conjecture on the energy conservation for solutions of Euler equations in bounded domains

Abstract

The Onsager's conjecture has two parts: conservation of energy, if the exponent is larger than $1/3$ and the possibility of dissipative Euler solutions, if the exponent is less or equal than $1/3$. The paper proves half of the conjecture, the conservation part, in bounded domains.

5 pages, to appear in Journal of Nonlinear Science

References in corpus (2)

• Onsager's Conjecture for the Incompressible Euler Equations in Bounded Domains
• Onsager's Conjecture with Physical Boundaries and an Application to the Vanishing Viscosity Limit

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• Onsager's Conjecture for the Incompressible Euler Equations in the Hölog Spaces $C_{\lambda }^{0,\alpha }(\bar{\Omega })$
• Construction of the Hodge-Neumann heat kernel, local Bernstein estimates, and Onsager's conjecture in fluid dynamics