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A Review for an Isotropic Landau Model

  • Maria Gualdani
  • Nicola Zamponi
Chapter
Part of the Springer INdAM Series book series (SINDAMS, volume 28)

Abstract

We consider the equation
$$\displaystyle u_t = \mathrm{div}\,(a[u]\nabla u - u\nabla a[u]),\qquad -\Delta a = u. $$
This model has attracted some attention in the recent years and several results are available in the literature. We review recent results on existence and smoothness of solutions and explain the open problems.

Keywords

Landau equation Coulomb potential Isotropic model Even solutions Weighted Poincaré and Sobolev inequalities Regularity estimates 

Notes

Acknowledgements

MPG is supported by NSF DMS-1514761. MPG would like to thank NCTS Mathematics Division Taipei for their kind hospitality. NZ acknowledges support from the Austrian Science Fund (FWF), grants P22108, P24304, W1245.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsGeorge Washington UniversityWashingtonUSA
  2. 2.Institute for Analysis and Scientific ComputingVienna University of TechnologyWienAustria

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