Onsager’s Conjecture with Physical Boundaries and an Application to the Vanishing Viscosity Limit

Bardos C, Titi ES, Wiedemann E (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Communications in Mathematical Physics Springer Verlag (Germany)

Book Volume: 370

Pages Range: 291-310

Journal Issue: 1

DOI: 10.1007/s00220-019-03493-6

Abstract

We consider the incompressible Euler equations in a bounded domain in three space dimensions. Recently, the first two authors proved Onsager’s conjecture for bounded domains, i.e., that the energy of a solution to these equations is conserved provided the solution is Hölder continuous with exponent greater than 1/3, uniformly up to the boundary. In this contribution we relax this assumption, requiring only interior Hölder regularity and continuity of the normal component of the energy flux near the boundary. The significance of this improvement is given by the fact that our new condition is consistent with the possible formation of a Prandtl-type boundary layer in the vanishing viscosity limit.

Authors with CRIS profile

Emil Wiedemann

Involved external institutions

Université Sorbonne Paris Cité FR France (FR) Texas A&M University US United States (USA) (US) Universität Ulm DE Germany (DE)

How to cite

APA:

Bardos, C., Titi, E.S., & Wiedemann, E. (2019). Onsager’s Conjecture with Physical Boundaries and an Application to the Vanishing Viscosity Limit. Communications in Mathematical Physics, 370(1), 291-310. https://dx.doi.org/10.1007/s00220-019-03493-6

MLA:

Bardos, Claude, Edriss S. Titi, and Emil Wiedemann. "Onsager’s Conjecture with Physical Boundaries and an Application to the Vanishing Viscosity Limit." Communications in Mathematical Physics 370.1 (2019): 291-310.

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