scholarly journals Global in time estimates for the spatially homogeneous Landau equation with soft potentials

2014 ◽  
Vol 266 (5) ◽  
pp. 3134-3155 ◽  
Author(s):  
Kung-Chien Wu
Keyword(s):  
Landau Equation ◽  
Time Estimates ◽  
Spatially Homogeneous

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.

scholarly journals A remark on the ultra-analytic smoothing properties of the spatially homogeneous Landau equation

2013 ◽  
Vol 6 (4) ◽  
pp. 715-727 ◽  
Author(s):  
Yoshinori Morimoto ◽  
◽  
Karel Pravda-Starov ◽  
Chao-Jiang Xu ◽  
◽  
...  
Keyword(s):  
Landau Equation ◽  
Spatially Homogeneous

ON THE SPATIALLY HOMOGENEOUS LANDAU EQUATION FOR MAXWELLIAN MOLECULES

1998 ◽  
Vol 08 (06) ◽  
pp. 957-983 ◽  
Author(s):  
C. VILLANI
Keyword(s):  
Cauchy Problem ◽  
Landau Equation ◽  
Explicit Solutions ◽  
The Cauchy Problem ◽  
Spatially Homogeneous ◽  
Maxwellian Molecules ◽  
Simplified Form

We establish a simplified form for the Landau equation with Maxwellian-type molecules. We study in details the Cauchy problem associated to this equation, and some qualitative features of the solution. Explicit solutions are given.

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