The rate of convergence for vanishing viscosity approximations to hyperbolic balance laws is established. The result applies to systems that are strictly hyperbolic and genuinely nonlinear with a source term satisfying a special mechanism that induces dissipation. The proof relies on error estimates that measure the interaction of waves. Shock waves are… (More)
We establish the global existence of weak solutions to a class of kinetic flocking equations. The models under conideration include the kinetic Cucker-Smale equation [6, 7] with possibly non-symmetric flocking potential, the Cucker-Smale equation with additional strong local alignment, and a newly proposed model by Motsch and Tadmor . The main tools… (More)
We consider a multidimensional model for the dynamics of liquid–vapor phase transitions. In the present context liquid and vapor are treated as different species with different volume fractions and different molecular weights. The model presented here is a prototype of a " binary fluid mixture, " and is formulated by the Navier Stokes equations in Euler… (More)
We establish a low Mach number limit for classical solutions over the whole space of a compressible fluid dynamic system that includes dispersive corrections to the Navier-Stokes equations. The limiting system is a ghost effect system . Our analysis builds upon the framework developed by Métivier and Schochet  and Alazard  for non-dispersive… (More)
We investigate the long time/small mean-free-path asymptotic behavior of the solutions of a Vlasov-Lévy-Fokker-Planck equation and show that the asymptotic dynamics for the VLFP are described by an anomalous diffusion equation.