Alexis F. VASSEUR

Professor

E-mail : vasseur@math.utexas.edu

• Current Vita

• Publications

Research topics :

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

Recent preprints :

2010

• Regularization in Keller-Segel type systems and the De Giorgi method. [pdf] (joint work with B.Perthame)
  To appear in CMS.

• Relative entropy and the stability of shocks and contact discontinuities for systems of conservation laws with non BV perturbations. [pdf] (joint work with Nicholas Leger)
  To appear in ARMA.

• The De Giorgi method for regularity of solutions of elliptic equations and its applications to fluid dynamics, (joint work with L.Caffarelli)
  To appear in Discrete and Continuous Dynamical Systems - Series S.

• Regularity theory for nonlinear integral operators , (joint work with L.Caffarelli, and Ch.-H.Chan)
  To appear in J. Amer. Math. Soc.

2009

• On global motions of a compressible barotropic and selfgravitating gas with density-dependent viscosities, (joint work with B. Ducomet, and Sarka Necasova)
  To appear in Z. Angew. Math. Phys.

• Weak in Space, Log in Time Improvement of the Ladyzenskaja-Prodi-Serrin Criteria, (joint work with C.Bjorland)
  to appear in Journal of Mathematical Fluid Mechanics.

• 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.
  To appear in Annales de l'IHP.

• 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)
  To appear in Adv. Math. Fluid Mech.

• 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.