L. A. Caffarelli et al: Nonlinear Partial Differential Equations

摘要

The present book consists of the lecture notes for four courses given at the school Topics in PDE's and Applications held at the FisyMat-Universidas de Granada and at the Center de Recerca Mathematica in Barcelona in 2008. The first lecture by L. Cafarelli and A. Vasseur introduce the classical De Giorgi truncation method and its applications to integral diffusions and the quasi-geostrophic equation. The second notes by F. Golse deal with the Boltzmann-Grad limit for Lorentz model for the the motion of electrons in a solid. The third lecture by Y. Guo is concerned with the Boltzmann equation in bounded domains in the near Mexwellian regime. Finally, the notes by C. Kenig introduce to a concentration-compactness/rigidity method to establish global well-posedness and scatter- ing for the energy critical nonlinear Schrodinger (both focusing and defocusing) and wave equations.