scholarly journals Analytic smoothing effect for the nonlinear Landau equation of Maxwellian molecules

2020 ◽  
Vol 13 (5) ◽  
pp. 951-978
Author(s):  
Yoshinori Morimoto ◽  
◽  
Chao-Jiang Xu ◽  
◽  
Keyword(s):  
Landau Equation ◽  
Smoothing Effect ◽  
Analytic Smoothing Effect ◽  
Maxwellian Molecules

DECREASE OF THE FISHER INFORMATION FOR SOLUTIONS OF THE SPATIALLY HOMOGENEOUS LANDAU EQUATION WITH MAXWELLIAN MOLECULES

2000 ◽  
Vol 10 (02) ◽  
pp. 153-161 ◽  
Author(s):  
C. VILLANI
Keyword(s):  
Numerical Simulation ◽  
Boltzmann Equation ◽  
Plasma Physics ◽  
Fisher Information ◽  
Landau Equation ◽  
Direct Proof ◽  
Homogeneous Boltzmann Equation ◽  
Spatially Homogeneous ◽  
Maxwellian Molecules ◽  
Spatially Homogeneous Boltzmann Equation

We give a direct proof of the fact that, in any dimension of the velocity space, Fisher's quantity of information is nonincreasing with time along solutions of the spatially homogeneous Landau equation for Maxwellian molecules. This property, which was first seen in numerical simulation in plasma physics, is linked with the theory of the spatially homogeneous Boltzmann equation.

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