Some remark on the existence of infinitely many nonphysical solutions to the incompressible Navier-Stokes equations

We prove that there exist infinitely many distributional solutions with infinite kinetic energy to both the incompressible Navier-Stokes equations in $ \mathbb{R}^2 $ and Burgers equation in $\mathbb{R} $ with vanishing initial data.

Detalles Bibliográficos
Autor: Scrobogna, S.
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2018
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/865
Acceso en línea:http://hdl.handle.net/20.500.11824/865
Access Level:acceso abierto
Palabra clave:Navier Stokes, distributional solutions
Descripción
Sumario:We prove that there exist infinitely many distributional solutions with infinite kinetic energy to both the incompressible Navier-Stokes equations in $ \mathbb{R}^2 $ and Burgers equation in $\mathbb{R} $ with vanishing initial data.