WIAS Preprint No. 2666, (2019)
Maximal dissipative solutions for incompressible fluid dynamics
Authors
- Lasarzik, Robert
ORCID: 0000-0002-1677-6925
2010 Mathematics Subject Classification
- 35D99 35Q30 76D05 76N10
Keywords
- Existence, uniqueness, Navier--Stokes, Euler, incompressible, fluid dynamics
DOI
Abstract
We introduce the new concept of maximal dissipative solutions for the Navier--Stokes and Euler equations and show that these solutions exist and the solution set is closed and convex. The concept of maximal dissipative solutions coincides with the concept of weak solutions as long as the weak solutions inherits enough regularity to be unique. A maximal dissipative solution is defined as the minimizer of a convex functional and we argue that this definition bears several advantages.
Appeared in
- ZAMP Z. Angew. Math. Phys., 73 (2022), pp. 1/1--1/21 (published online on 11.11.2021), DOI 10.1007/s00033-021-01628-1 .
Download Documents