Alexis F. VASSEUR

Associate Professor

E-mail : vasseur@math.utexas.edu
Office : RLM: 11.171
Phone : (512) 471 2363
Fax : (512) 471 9038

• Current Vita

• Publications

Research topics :

Partial Differential Equations
Navier-Stokes equations
Hyperbolic conservation laws
Kinetic equations, hydrodynamic limits

Recent preprints :

2009

• Quantum Hydrodynamics with Trajectories: The Nonlinear Conservation Form Mixed/Discontinuous Galerkin Method with Applications in Chemistry , (joint work with J. Evans, C. Michoski, P. Schmitz)
  to appear in Journal of Computational Physics.

• On spherically symmetric motions of a viscous compressible barotropic and self-graviting gas, (joint work with B. Ducomet, S. Necasova)
  To appear in Journal of Mathematical Fluid Mechanics.

• Higher derivatives estimate for the 3D Navier-Stokes equation.
  

• Global existence of solutions to one-dimensional viscous quantum hydrodynamic equations. (joint work with I. Gamba and A. Jungel)
  To appear in Journal of Differential Equations.

• Global regularity of solutions to systems of reaction-diffusion wity sub-quadratic growth in any dimension. (joint work with Cristina Caputo)
  To appear in CPDE.

2008

• From discrete velocity Boltzmann equations to gas dynamics before shocks. (joint work with F.Berthelin and A.E.Tzavaras)
  To appear in JSP.

• Rigorous derivation of the Kinetic/Fluid coupling involving a Kinetic layer on a toy problem.
  To appear in ARMA.

• New perspectives in fluid dynamics: Mathematical analysis of a model proposed by Howard Brenner. (joint work with E.Feireisl)

• Existence and Uniqueness of strong solutions for a compressible multiphase Navier-Stokes Miscible Fluid-Flow Problem in dimension 1. (joint work with C.Michoski)
  To appear in Mathematical Models and Methods in Applied Sciences.
  

• Boundary value problems for the stationary Vlasov-Boltzmann-Poisson equation (joint work with M.Bostan, M.Gamba and Th. Goudon)
  To appear in the Indiana University Mathematics Journal.

• Study of a generalized fragmentation model for sprays (joint work with N.Leger)
  To appear in the Journal of Hyperbolic Differential Equations.
  

2007

• A bound from below for the temperature in compressible Navier-Stokes equations. (joint work with A.Mellet)
  To appear in Monatshefte fur Mathematik.

• Recent results on hydrodynamic limits, Chapter for Handbook on Evolutionary Differential Equations.

• Regularity criterion for 3D Navier-Stokes equations in terms of the direction of the velocity.
  To appear in Applications of Mathematics

• Log improvement of the Prodi-Serrin criteria for Navier-Stokes equations.
  (joint work with Ch.-H. Chan).
  To appear in the Methods and Applications of Analysis.
  

• Regularity analysis for systems of reaction-diffusion equations.
  (joint work with Th. Goudon)
  To appear in les annales de l'Ecole Normale Superieure.
  

2006

• Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
  (joint work with L.Caffarelli). To appear in Annals of Math.

• L^p estimates for quantities advected by a compressible flow
  (joint work with A.Mellet) To appear in JMAA.

• Global weak solutions for a Vlasov-Fokker-Planck/Navier-Stokes system of equations
  (joint work with A.Mellet) To appear in Math. Models Methods Appl. Sci.

• Asymptotic analysis for a Vlasov-Fokker-Planck/Compressible Navier-Stokes system of equations
  (joint work with A.Mellet) To appear in CMP.

• Strong traces for solutions to scalar conservation laws with general flux (joint work with Y.-S.Kwon)
  To appear in ARMA.
  

• Existence and uniqueness of global strong solutions for one-dimensional compressible Navier-Stokes equations
  (joint work with A.Mellet) To appear in SIAM J. Math. Anal.
  

2005

• On the barotropic compressible Navier-Stokes equations (joint work with A.Mellet)
  To appear in CPDE.
  

• A new proof of partial regularity of solutions to Navier-Stokes equations.
  To appear in NoDEA.
  

• Homogenization of a nonlinear transport equation. (joint work with A.Mellet)
  To appear in Asymptotic Analysis.