# American Institute of Mathematical Sciences

January  2009, 24(1): 1-11. doi: 10.3934/dcds.2009.24.1

## Littlewood-Paley theory and regularity issues in Boltzmann homogeneous equations II. Non cutoff case and non Maxwellian molecules

 1 IRENAV, French Naval Academy, 29240 BREST ARMEES 2 MAPMO UMR 6628, Universit´e d’Orléans, BP 6759, 45067 Orléans Cedex 2, France

Received  October 2007 Revised  March 2008 Published  January 2009

We use Littlewood-Paley theory for the analysis of regularization properties of weak solutions of the homogeneous Boltzmann equation. For non cutoff and non Maxwellian molecules, we show that such solutions are smoother than the initial data. In particular, our method applies to any weak solution, though we assume that it belongs to a weighted $L^2$ space.
Citation: Radjesvarane Alexandre, Mouhamad Elsafadi. Littlewood-Paley theory and regularity issues in Boltzmann homogeneous equations II. Non cutoff case and non Maxwellian molecules. Discrete & Continuous Dynamical Systems - A, 2009, 24 (1) : 1-11. doi: 10.3934/dcds.2009.24.1
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