GEVREY SMOOTHING FOR WEAK SOLUTIONS OF THE FULLY NONLINEAR HOMOGENEOUS BOLTZMANN AND KAC EQUATIONS WITHOUT CUTOFF FOR MAXWELLIAN MOLECULESReportar como inadecuado




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1 CPT - E9 Dynamique quantique et analyse spectrale CPT - Centre de Physique Théorique - UMR 7332 2 CPT - Centre de Physique Théorique - UMR 7332 3 KIT - Karlsruhe Institute of Technology Karlsruhe

Abstract : It has long been suspected that the non-cutoff Boltzmann operator has similar coerciv-ity properties as a fractional Laplacian. This has led to the hope that the homogenous Boltzmann equation enjoys similar regularity properties as the heat equation with a fractional Laplacian. In particular , the weak solution of the fully nonlinear non-cutoff homogenous Boltzmann equation with initial datum in L 1 2 R d ∩ L log LR d, i.e., finite mass, energy and entropy, should immediately become Gevrey regular for strictly positive times. We prove this conjecture for Maxwellian molecules.

Keywords : Non-cutoff homogen-eous Kac equation Gevrey regularity Non-cutoff homogeneous Boltzmann equation Maxwellian molecules Contents





Autor: Jean-Marie Barbaroux - Dirk Hundertmark - Tobias Ried - Semjon Vugalter -

Fuente: https://hal.archives-ouvertes.fr/



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