Maximal dissipative solutions for incompressible fluid dynamics
- Lasarzik, Robert
2010 Mathematics Subject Classification
- 35D99 35Q30 76D05 76N10
- Existence, uniqueness, Navier--Stokes, Euler, incompressible, fluid dynamics
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.