Maximal dissipative solutions for incompressible fluid dynamics

Abstract

We introduce the new concept of maximal dissipative solutions for a general class of isothermal GENERIC systems. Under certain assumption, we show that maximal dissipative solutions are well posed as long as the bigger class of dissipative solutions is non-empty. Applying this result to the Navier--Stokes and Euler equations, we infer global well-posedness of maximal dissipative solutions for these systems. 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.

References in corpus (5)

• Dissipative solutions and semiflow selection for the complete Euler system
• Dissipative solution to the Ericksen-Leslie system equipped with the Oseen-Frank energy
• Approximation and optimal control of dissipative solutions to the Ericksen--Leslie system
• Analysis of a thermodynamically consistent Navier--Stokes--Cahn--Hilliard model
• Weak solutions and weak-strong uniqueness for a thermodynamically consistent phase-field model

Cited by in corpus (4)

• Weak-strong uniqueness and energy-variational solutions for a class of viscoelastoplastic fluid models
• Non-Uniqueness in Plane Fluid Flows
• Maximal turbulence as a selection criterion for measure-valued solutions
• Analysis and numerical approximation of energy-variational solutions to the Ericksen--Leslie equations