Mathematics and turbulence: where do we stand?

The incompressible Euler limit of the Boltzmann equation with accommodation boundary condition

(2013) Claude Bardos et al.   Communications in Mathematical Sciences

On the local existence of analytic solutions to the Prandtl boundary layer equations

(2013) Igor Kukavica et al.   Communications in Mathematical Sciences

The $h$-principle and the equations of fluid dynamics

(2012) Camillo De Lellis et al.   BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY

The vanishing viscosity as a selection principle for the Euler equations: The case of 3D shear flow

(2012) Claude Bardos et al.   COMPTES RENDUS MATHEMATIQUE

Vanishing Viscous Limits for 3D Navier–Stokes Equations with a Navier-Slip Boundary Condition

(2012) Lizhen Wang et al.   Journal of Mathematical Fluid Mechanics

A missed persistence property for the Euler equations and its effect on inviscid limits

(2012) H Beirão da Veiga et al.   NONLINEARITY

Existence of weak solutions for the incompressible Euler equations

(2011) Emil Wiedemann   ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE

Global Regularity Criterion for the 3D Navier–Stokes Equations Involving One Entry of the Velocity Gradient Tensor

(2011) Chongsheng Cao et al.   ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS

Weak solutions to the incompressible Euler equations with vortex sheet initial data

(2011) László Székelyhidi   COMPTES RENDUS MATHEMATIQUE

On the analyticity and Gevrey-class regularity up to the boundary for the Euler equations

(2011) Igor Kukavica et al.   NONLINEARITY

Examples of boundary layers associated with the incompressible Navier-Stokes equations

(2010) Xiaoming Wang   CHINESE ANNALS OF MATHEMATICS SERIES B

On universal relations in 2-D turbulence

(2010) Nusret Balci et al.   DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

The 3-D Inviscid Limit Result Under Slip Boundary Conditions. A Negative Answer

(2010) H. Beirão da Veiga et al.   Journal of Mathematical Fluid Mechanics

On the Convergence Rate of the Euler-α, an Inviscid Second-Grade Complex Fluid, Model to the Euler Equations

(2010) Jasmine S. Linshiz et al.   JOURNAL OF STATISTICAL PHYSICS

On the ill-posedness of the Prandtl equation

(2010) David Gérard-Varet et al.   JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY

Loss of smoothness and energy conserving rough weak solutions for the $3d$ Euler equations

(2010) E. Titi et al.   Discrete and Continuous Dynamical Systems-Series S

Global regularity and convergence of a Birkhoff-Rott-α approximation of the dynamics of vortex sheets of the two-dimensional Euler equations

(2009) Claude Bardos et al.   COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS

Global Existence and Uniqueness of Weak Solutions of Three-Dimensional Euler Equations with Helical Symmetry in the Absence of Vorticity Stretching

(2009) Boris Ettinger et al.   SIAM JOURNAL ON MATHEMATICAL ANALYSIS

On Admissibility Criteria for Weak Solutions of the Euler Equations

(2008) Camillo de Lellis et al.   ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS

Regularity criteria for the three-dimensional Navier-Stokes equations

(2008) Chongsheng Cao et al.   INDIANA UNIVERSITY MATHEMATICS JOURNAL

Some specific mathematical constraints on 2D turbulence

(2008) R. Dascaliuc et al.   PHYSICA D-NONLINEAR PHENOMENA