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- Title
Onsager's Conjecture with Physical Boundaries and an Application to the Vanishing Viscosity Limit.
- Authors
Bardos, Claude; Titi, Edriss S.; Wiedemann, Emil
- 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.
- Subjects
HOLDER spaces; VISCOSITY; BOUNDARY layer (Aerodynamics); FLUX (Energy); LOGICAL prediction; EULER equations
- Publication
Communications in Mathematical Physics, 2019, Vol 370, Issue 1, p291
- ISSN
0010-3616
- Publication type
Article
- DOI
10.1007/s00220-019-03493-6