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AVERAGING OF HAMILTONIAN FLOWS WITH AN ERGODIC COMPONENT
ERGODIC COMPONENT Unperturbed flow
2015/9/29
We consider a process on T2, which consists of fast motion along the
stream lines of an incompressible periodic vector field perturbed by white
noise. It gives rise to a process on the graph n...
Global well-posedness and stability of electro-kinetic flows
Navier-Stokes-Nernst-Planck-Poisson equations local and global well-posedness exponential stability of steady states
2012/6/27
We consider a coupled system of Navier-Stokes and Nernst-Planck equations, describing the evolution of the velocity and the concentration fields of dissolved constituents in an electrolyte solution. M...
Compressible fluid flows driven by stochastic forcing
stochastic Navier-Stokes equations compressible fluid random driving force
2012/6/21
We consider the Navier-Stokes system describing the motion of a compressible barotropic fluid driven by stochastic external forces. Our approach is semi-deterministic, based on solving the system for ...
Fluid accumulation in thin-film flows driven by surface tension and gravity (I): Rigorous analysis of a drainage equation
Fluid accumulation surface tension and gravity drainage equation
2011/9/23
Abstract: We derive a boundary layer equation describing accumulation regions within a thin-film approximation framework where gravity and surface tension balance. As part of the analysis of this prob...
A Blow-up Criterion for Two Dimensional Compressible Viscous Heat-Conductive Flows
Blow-up Criterion Two Dimensional Compressible Viscous Heat-Conductive Flows Analysis of PDEs
2011/9/19
Abstract: We establish a blow-up criterion in terms of the upper bound of the density and temperature for the strong solution to 2D compressible viscous heat-conductive flows. The initial vacuum is al...
A Hamilton-Jacobi approach to junction problems and application to traffic flows
Hamilton-Jacobi equations, discontinuous Hamiltonians, viscosity solutions, optimal control, traffic problems, junctions
2011/9/13
Abstract: This paper is concerned with the study of a model case of first order Hamilton-Jacobi equations posed on a "junction", that is to say the union of a finite number of half-lines with a unique...
Unsteady mixed flows in non uniform closed water pipes: a Full Kinetic Appraoch
Mixed flows in closed water pipes drying and flooding flows kinetic interpretation of conservation laws
2011/8/26
Abstract: We recall the \PFS} model constructed for the modeling of unsteady mixed flows in closed water pipes where transition points between the free surface and pressurized flow are treated as a fr...
Large Eddy Simulation for Turbulent Flows with Critical Regularization
Turbulence models existence weak solution
2011/8/29
Abstract: In this paper, we establish the existence of a unique "regular" weak solution to the Large Eddy Simulation (LES) models of turbulence with critical regularization. We first consider the crit...
On the lack of dispersion for a class of magnetic Dirac flows
Dirac equation Strichartz estimates dispersive equations magnetic potential
2011/8/25
Abstract: We show that global Strichartz estimates for magnetic Dirac operators generally fails, if the potentials do not decay fast enough at in?nity. In order to prove this, we construct some explic...
On the singular set of mean curvature flows with Neumann free boundary conditions
singular set of mean curvature flows Neumann free boundary conditions
2011/1/17
We consider n-dimensional hypersurfaces flowing by mean curvature flow with Neumann free
boundary conditions supported on a smooth support surface. We show that the Hausdorff n-measure of the singula...