Sur la propagation de quasi-singularités
The Eulerian limit and the slip boundary conditions-admissible irregularity of the boundary
We investigate the inviscid limit for the stationary Navier-Stokes equations in a two dimensional bounded domain with slip boundary conditions admitting nontrivial inflow across the boundary. We analyze admissible regularity of the boundary necessary to obtain convergence to a solution of the Euler system. The main result says that the boundary of the domain must be at least C²-piecewise smooth with possible interior angles between regular components less than π.
Two dimensional incompressible ideal flow around a thin obstacle tending to a curve
Uniqueness and radial symmetry for an inverse elliptic equation.
Zero-Dissipation Limit for Nonlinear Waves
Evolution equations featuring nonlinearity, dispersion and dissipation are considered here. For classes of such equations that include the Korteweg-de Vries-Burgers equation and the BBM-Burgers equation, the zero dissipation limit is studied. Uniform bounds independent of the dissipation coefficient are derived and zero dissipation limit results with optimal convergence rates are established.