WIAS Preprint No. 2834, (2021)
On the existence of weak solutions in the context of multidimensional incompressible fluid dynamics
Authors
- Lasarzik, Robert
ORCID: 0000-0002-1677-6925
2020 Mathematics Subject Classification
- 35D99 35Q30 35Q31 76D05
Keywords
- Existence, uniqueness, Navier--Stokes, Euler, incompressible, fluid dynamics, weak solutions, dissipative solutions
DOI
Abstract
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.
Appeared in
- Math. Methods Appl. Sci. (published online on 27.11.2023), DOI 10.1002/mma.9816 with changed title ``On the existence of energy-variational solutions in the context of multidimensional incompressible fluid dynamics''.
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