Nonlinear Partial Differential Equations

1. Front Matter

   Pages i-viii

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2. The De Giorgi Method for Nonlocal Fluid Dynamics

   • Luis A. Caffarelli, Alexis Vasseur

   Pages 1-38

3. Recent Results on the Periodic Lorentz Gas

   • François Golse

   Pages 39-99

4. The Boltzmann Equation in Bounded Domains

   • Yan Guo

   Pages 101-115

5. The Concentration-Compactness Rigidity Method for Critical Dispersive and Wave Equations

   • Carlos E. Kenig

   Pages 117-149

The book covers several topics of current interest in the field of nonlinear partial differential equations and their applications to the physics of continuous media and particle interactions. It treats the quasigeostrophic equation, integral diffusions, periodic Lorentz gas, Boltzmann equation, and critical dispersive nonlinear Schrödinger and wave equations. The book describes in a careful and expository manner several powerful methods from recent top research articles.

• Boltzmann equations
• hyperbolic equations
• statistical mechanics
• partial differential equations

From the reviews:

“Its aim was to provide an overview of some of the most important current lines of research in the field of nonlinear PDE. … Both for novices and experts in the areas covered the contributions provide deep insights into the guiding principles and relevant methods of these active fields of current research.” (M. Kunzinger, Monatshefte für Mathematik, Vol. 171 (1), July, 2013)

• College of Natural Sciences, Dept. Mathematics, University of Texas, Austin, USA

  Luis A. Caffarelli

• , Centre de Mathématiques L. Schwartz, Ecole Polytechnique, Palaiseau Cedex, France

  François Golse

• , Division of Applied Mathematics, Brown University, Providence, USA

  Yan Guo

• Dept. Mathematics, University of Chicago, Chicago, USA

  Carlos E. Kenig

• , Department of Mathematics, University of Texas at Austin, Austin, USA

  Alexis Vasseur

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