Displaying similar documents to “On a variant of Korn's inequality arising in statistical mechanics”

Impact of the variations of the mixing length in a first order turbulent closure system

Françoise Brossier, Roger Lewandowski (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

This paper is devoted to the study of a turbulent circulation model. Equations are derived from the “Navier-Stokes turbulent kinetic energy” system. Some simplifications are performed but attention is focused on non linearities linked to turbulent eddy viscosity  ν t . The mixing length acts as a parameter which controls the turbulent part in ν t . The main theoretical results that we have obtained concern the uniqueness of the solution for bounded eddy viscosities and small values of ...

Relaxation of singular functionals defined on Sobolev spaces

Hafedh Ben Belgacem (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

In this paper, we consider a Borel measurable function on the space of m × n matrices f : M m × n ¯ taking the value + , such that its rank-one-convex envelope R f is finite and satisfies for some fixed p > 1 : - c 0 R f ( F ) c ( 1 + F p ) for all F M m × n , where c , c 0 > 0 . Let Ø be a given regular bounded open domain of n . We define on W 1 , p ( Ø ; m ) the functional I ( u ) = Ø f ( u ( x ) ) d x . Then, under some technical restrictions on f , we show that the relaxed functional I ¯ for the weak topology of W 1 , p ( Ø ; m ) has the integral representation: I ¯ ( u ) = Ø Q [ R f ] ( u ( x ) ) d x , where for a given function g , Q g denotes...