scholarly journals From a Non-Markovian System to the Landau Equation

2018 ◽  
Vol 361 (1) ◽  
pp. 239-287 ◽  
Author(s):  
Juan J. L. Velázquez ◽  
Raphael Winter
Keyword(s):  
Landau Equation ◽  
Markovian System

scholarly journals About the Use of Entropy Production for the Landau–Fermi–Dirac Equation

2021 ◽  
Vol 183 (1) ◽  
Author(s):  
R. Alonso ◽  
V. Bagland ◽  
L. Desvillettes ◽  
B. Lods
Keyword(s):  
Dirac Equation ◽  
Classical Limit ◽  
Large Time ◽  
A Priori Estimates ◽  
Landau Equation ◽  
A Priori ◽  
Time Behaviour ◽  
Entropy Dissipation ◽  
Priori Estimates ◽  
Potential Case

AbstractIn this paper, we present new estimates for the entropy dissipation of the Landau–Fermi–Dirac equation (with hard or moderately soft potentials) in terms of a weighted relative Fisher information adapted to this equation. Such estimates are used for studying the large time behaviour of the equation, as well as for providing new a priori estimates (in the soft potential case). An important feature of such estimates is that they are uniform with respect to the quantum parameter. Consequently, the same estimations are recovered for the classical limit, that is the Landau equation.

scholarly journals Correction to: The Landau Equation with the Specular Reflection Boundary Condition

2021 ◽  
Vol 240 (1) ◽  
pp. 605-626
Author(s):  
Yan Guo ◽  
Hyung Ju Hwang ◽  
Jin Woo Jang ◽  
Zhimeng Ouyang
Keyword(s):  
Boundary Condition ◽  
Specular Reflection ◽  
Landau Equation ◽  
Reflection Boundary

A WEAKLY NONLINEAR INSTABILITY OF MISCIBLE DISPLACEMENTS IN A RECTILINEAR POROUS MEDIA FLOW

1994 ◽  
Vol 04 (05) ◽  
pp. 1319-1328 ◽  
Author(s):  
WILLIAM B. ZIMMERMAN
Keyword(s):  
Linear Theory ◽  
Landau Equation ◽  
Separation Of Variables ◽  
Finite Amplitude ◽  
Linear Stability Theory ◽  
Porous Media Flow ◽  
Perturbation Scheme ◽  
Viscous Effects ◽  
Regular Perturbation ◽  
Displacement Front

The linear stability theory of Tan & Homsy [1986] is extended to include the effects of weak nonlinear coupling between mass flux and viscous effects when the viscous fingers grow from a slowly diffusing, nearly flat displacement front. A regular perturbation scheme combined with a similarity-separation of variables technique leads to a Landau equation for the amplitude of the disturbance. The Landau constant has a simple pole for a given wavenumber within the linear theory cutoff wavenumber for growth. An argument is given that this pole leads to pairing of fingers while the instability remains small. Comparison of the length scale of the pole of the Landau constant with experimental measurements of finger scale shows good agreement where plausibly finite-amplitude effects might come into play, but with the linear theory otherwise.

Spiral Solutions of the Two-Dimensional Complex Ginzburg–Landau Equation

2001 ◽  
Vol 35 (2) ◽  
pp. 159-161
Author(s):  
Liu Shi-Da ◽  
Liu Shi-Kuo ◽  
Fu Zun-Tao ◽  
Zhao Qiang
Keyword(s):  
Landau Equation ◽  
Two Dimensional ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation
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