Some Variational and Stochastic Methods for the Euler Equations of Incompressible Fluid Dynamics and Related Models

2017 ◽  
pp. 169-189 ◽  
Author(s):  
Yann Brenier
Keyword(s):  
Fluid Dynamics ◽  
Incompressible Fluid ◽  
Euler Equations ◽  
Stochastic Methods

scholarly journals Maximally dissipative solutions for incompressible fluid dynamics

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
Robert Lasarzik
Keyword(s):  
Fluid Dynamics ◽  
Incompressible Fluid ◽  
Euler Equations ◽  
Weak Solutions ◽  
General Class ◽  
Navier Stokes ◽  
Well Posedness ◽  
Dissipative Solutions ◽  
Well Posed

AbstractWe introduce the new concept of maximally dissipative solutions for a general class of isothermal GENERIC systems. Under certain assumptions, we show that maximally 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 maximally dissipative solutions for these systems. The concept of maximally dissipative solutions coincides with the concept of weak solutions as long as the weak solutions inherits enough regularity to be unique.

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