PreprintAll rights reserved2021Published
On the existence of weak solutions in the context of multidimensional incompressible fluid dynamics
- ORCID
- 0000-0002-1677-6925
- Affiliation
- Weierstraß-Institut für Angewandte Analysis und Stochastik, Berlin
We define the concept of energy-variational solutions for the Navier--Stokes and Euler equations. This concept is shown to be equivalent to weak solutions with energy conservation. Via a standard Galerkin discretization, we prove the existence of energy-variational solutions and thus weak solutions in any space dimension for the Navier--Stokes equations. In the limit of vanishing viscosity the same assertions are deduced for the incompressible Euler system. Via the selection criterion of maximal dissipation we deduce well-posedness for these equations.
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