Some remarks on global solutions to nonlinear dissipative mildly degenerate Kirchhoff strings
Some remarks on gradient estimates for heat kernels.
Some remarks on infinite-dimensional nonlinear elliptic problems.
Some remarks on Kato's inequality.
Some remarks on -valued functions
Some remarks on multidimensional systems of conservation laws
This note is concerned with the Cauchy problem for hyperbolic systems of conservation laws in several space dimensions. We first discuss an example of ill-posedness, for a special system having a radial symmetry property. Some conjectures are formulated, on the compactness of the set of flow maps generated by vector fields with bounded variation.
Some remarks on Prandtl system
The purpose of this paper is to correct some drawbacks in the proof of the well-known Boundary Layer Theory in Oleinik’s book. The Prandtl system for a nonstationary layer arising in an axially symmetric incopressible flow past a solid body is analyzed.
Some remarks on the asymptotic equivalence
Some Remarks on the Boundary Conditions in the Theory of Navier-Stokes Equations
This article addresses some theoretical questions related to the choice of boundary conditions, which are essential for modelling and numerical computing in mathematical fluids mechanics. Unlike the standard choice of the well known non slip boundary conditions, we emphasize three selected sets of slip conditions, and particularly stress on the interaction between the appropriate functional setting and the status of these conditions.
Some remarks on the boundary regularity for minima of variational problems with obstacles.
Some remarks on the continuity equation
This text is the act of a talk given november 18 2008 at the seminar PDE of Ecole Polytechnique. The text is not completely faithfull to the oral exposition for I have taken this opportunity to present the proofs of some results that are not easy to find in the literature. On the other hand, I have been less precise on the material for which I found good references. Most of the novelties presented here come from a joined work with Luigi Ambrosio.
Some remarks on the Galerkin approximation of parabolic equations
Some Remarks on the Homogenization of the Dam Problem.
Some remarks on the KP system of the Camassa-Holm hierarchy.
Some remarks on the multi-dimensional Borg-Levinson theorem
Some remarks on the Navier-Stokes equations with regularity in one direction
We review the developments of the regularity criteria for the Navier-Stokes equations, and make some further improvements.
Some remarks on the non-uniqueness of the stationary solutions of Navier-Stokes equations.
Some remarks on the number of solutions of some nonlinear elliptic problems
Some remarks on the regularity of minimizers of integrals with anisotropic growth
We prove higher integrability for minimizers of some integrals of the calculus of variations; such an improved integrability allows us to get existence of weak second derivatives.
Some remarks on the regularity of weak solutions of degenerate elliptic systems.