On the regularity of the pressure field of Brenier’s weak solutions to incompressible Euler equations

2007 ◽  
Vol 31 (4) ◽  
pp. 497-509 ◽  
Author(s):  
Luigi Ambrosio ◽  
Alessio Figalli
Keyword(s):  
Euler Equations ◽  
Weak Solutions ◽  
Pressure Field ◽  
Incompressible Euler Equations ◽  
Incompressible Euler

Introduction

2017 ◽  
Author(s):  
Philip Isett
Keyword(s):  
Euler Equations ◽  
Ideal Fluid ◽  
Weak Solutions ◽  
Modern Language ◽  
Incompressible Euler Equations ◽  
Spatial Dimensions ◽  
Periodic Weak Solutions ◽  
Incompressible Euler ◽  
Onsager’S Conjecture

In the paper [DLS13], De Lellis and Székelyhidi introduce a method for constructing periodic weak solutions to the incompressible Euler equations{∂tv+div v⊗v+∇p=0                       div v=0in three spatial dimensions that are continuous but do not conserve energy. The motivation for constructing such solutions comes from a conjecture of Lars Onsager [Ons49] on the theory of turbulence in an ideal fluid. In the modern language of PDE, Onsager's conjecture can be translated as follows....

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