Navier-Stokes equations with potentials.
Navier–Stokes regularization of multidimensional Euler shocks
Nearly concentric Korteweg-de Vries equation and periodic traveling wave solution.
Néel and Cross-Tie wall energies for planar micromagnetic configurations
We study a two-dimensional model for micromagnetics, which consists in an energy functional over -valued vector fields. Bounded-energy configurations tend to be planar, except in small regions which can be described as vortices (Bloch lines in physics). As the characteristic “exchange-length” tends to 0, they converge to planar divergence-free unit norm vector fields which jump along line singularities. We derive lower bounds for the energy, which are explicit functions of the jumps of the limit....
Néel and Cross-Tie Wall Energies for Planar Micromagnetic Configurations
We study a two-dimensional model for micromagnetics, which consists in an energy functional over S2-valued vector fields. Bounded-energy configurations tend to be planar, except in small regions which can be described as vortices (Bloch lines in physics). As the characteristic “exchange-length” tends to 0, they converge to planar divergence-free unit norm vector fields which jump along line singularities. We derive lower bounds for the energy, which are explicit functions of the jumps of the limit....
Nested axi-symmetric vortex rings
New efficient boundary conditions for incompressible Navier-Stokes equations : a well-posedness result
New exact solutions for the -dimensional Broer-Kaup-Kupershmidt equations.
New exact solutions of the Brusselator reaction diffusion model using the exp-function method.
New exact traveling wave solutions for compound KdV-Burgers equations in mathematical physics.
New exact traveling wave solutions of the ()-dimensional Zakharov-Kuznetsov (ZK) equation.
New explicit and exact solutions for the Nizhnik-Novikov-Vesselov equation.
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 in Velocity Averaging
This paper discusses two new directions in velocity averaging. One is an improvement of the known velocity averaging results for functions. The other shows how to adapt some of the ideas of velocity averaging to a situation that is essentially a new formulation of the Vlasov-Maxwell system.
New solitons and periodic solutions for Thekadomtsev-Petviashvili equation.
New unilateral problems in stratigraphy
This work deals with the study of some stratigraphic models for the formation of geological basins under a maximal erosion rate constrain. It leads to introduce differential inclusions of degenerated hyperbolic-parabolic type , where H is the maximal monotonous graph of the Heaviside function and E is a given non-negative function. Firstly, we present the new and realistic models and an original mathematical formulation, taking into account the weather-limited rate constraint in the conservation...
Ninth international school on mathematical theory in fluid mechanics
No production of entropy in the Euler fluid
We derive the Euler equations as the hydrodynamic limit of a stochastic model of a hard-sphere gas. We show that the system does not produce entropy.
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.