Navier-Stokes equation with slip-like boundary condition.
New regularity results for a generic model equation in exterior 3D domains
We consider a generic scalar model for the Oseen equations in an exterior three-dimensional domain. We assume the case of a non-constant coefficient function. Using a variational approach we prove new regularity properties of a weak solution whose existence and uniqueness in anisotropically weighted Sobolev spaces were proved in [10]. Because we use some facts and technical tools proved in the above mentioned paper, we give also a brief review of its results and methods.
New results on the Burgers and the linear heat equations in unbounded domains.
We consider the Burgers equation and prove a property which seems to have been unobserved until now: there is no limitation on the growth of the nonnegative initial datum u0(x) at infinity when the problem is formulated on unbounded intervals, as, e.g. (0 +∞), and the solution is unique without prescribing its behaviour at infinity. We also consider the associate stationary problem. Finally, some applications to the linear heat equation with boundary conditions of Robin type are also given.
Nombres de Reynolds, stabilité et Navier-Stokes
Non blow-up of the 3D ideal magnetohydrodynamics equations for a class of three-dimensional initial data in cylindrical domains.
Non-Newtonian fluids and function spaces
In this note we give an overview of recent results in the theory of electrorheological fluids and the theory of function spaces with variable exponents. Moreover, we present a detailed and self-contained exposition of shifted -functions that are used in the studies of generalized Newtonian fluids and problems with -structure.
Numerical modelling of algebraic closure models of oceanic turbulent mixing layers
We introduce in this paper some elements for the mathematical and numerical analysis of algebraic turbulence models for oceanic surface mixing layers. In these models the turbulent diffusions are parameterized by means of the gradient Richardson number, that measures the balance between stabilizing buoyancy forces and destabilizing shearing forces. We analyze the existence and linear exponential asymptotic stability of continuous and discrete equilibria states. We also analyze the well-posedness...