The Landau Equation

  • Herbert Spohn
Part of the Texts and Monographs in Physics book series (TMP)


A weakly coupled gas/fluid is governed on the macroscopic scale by the Landau equation
$$ \frac{\partial }{{\partial t}}{{f}_{t}}\left( {x,v} \right) + v\cdot {{\nabla }_{x}}{{f}_{t}}\left( {x,v} \right)\,{\text{ = }}\alpha \sum\limits_{{i,j = 1}}^{3} {\frac{\partial }{{\partial vi}}} \int {{{d}^{3}}} w\left[ {{{{\left| {v - w} \right|}}^{{ - 3}}}\left( {{{{\left| {v - w} \right|}}^{2}}{{\delta }_{{ij}}} - {{{\left( {v - w} \right)}}_{i}}{{{\left( {v - w} \right)}}_{j}}} \right) \times \left( {\frac{\partial }{{\partial {{v}_{j}}}} - \frac{\partial }{{\partial {{v}_{j}}}}} \right){{f}_{t}}\left( {x,w} \right){{f}_{t}}\left( {x,v} \right)} \right]. $$

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Herbert Spohn
    • 1
  1. 1.Theoretische PhysikLudwig-Maximilians-Universität MünchenMünchen 2Fed. Rep. of Germany

Personalised recommendations