ENERGY CONSERVATION FOR 2D EULER WITH VORTICITY IN L(log L)α*
In these notes we discuss the conservation of the energy for weak solutions of the twodimensional incompressible Euler equations. Weak solutions with vorticity in (Formula presented) with p > 3/2 are always conservative, while for less integrable vorticity the conservation of the energy may depen...
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Basque Center for Applied Mathematics (BCAM) |
| Repositorio: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/1486 |
| Acceso en línea: | http://hdl.handle.net/20.500.11824/1486 |
| Access Level: | acceso abierto |
| Palabra clave: | 2D Euler equations conservation of energy vanishing viscosity vortex methods |
| Sumario: | In these notes we discuss the conservation of the energy for weak solutions of the twodimensional incompressible Euler equations. Weak solutions with vorticity in (Formula presented) with p > 3/2 are always conservative, while for less integrable vorticity the conservation of the energy may depend on the approximation method used to construct the solution. Here we prove that the canonical approximations introduced by DiPerna and Majda provide conservative solutions when the initial vorticity is in the class L(logL)α with α > 1/2. |
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