Global solution of the initial value problem for the Boltzmann equation near a local Maxwellian

1988 ◽  
Vol 102 (3) ◽  
pp. 231-241 ◽  
Author(s):  
G. Toscani
Keyword(s):  
Boltzmann Equation ◽  
Global Solution ◽  
Initial Value Problem ◽  
Initial Value ◽  
The Boltzmann Equation

On the initial value problem for the Boltzmann equation with a force term

1989 ◽  
Vol 18 (1) ◽  
pp. 87-102 ◽  
Author(s):  
N. Bellomo ◽  
M. Lachowicz ◽  
A. Palczewski ◽  
G. Toscani
Keyword(s):  
Boltzmann Equation ◽  
Initial Value Problem ◽  
Force Term ◽  
Initial Value ◽  
The Boltzmann Equation

SOME MATHEMATICAL RESULTS ON THE ASYMPTOTIC BEHAVIOUR OF THE SOLUTIONS TO THE INITIAL VALUE PROBLEM FOR THE ENSKOG EQUATION

1989 ◽  
Vol 01 (02n03) ◽  
pp. 183-196
Author(s):  
N. BELLOMO ◽  
M. LACHOWICZ
Keyword(s):  
Boltzmann Equation ◽  
Asymptotic Behaviour ◽  
Knudsen Number ◽  
Initial Value Problem ◽  
Hydrodynamic Limit ◽  
Enskog Equation ◽  
Asymptotic Equivalence ◽  
Initial Value ◽  
The Boltzmann Equation

This paper deals with the analysis of some mathematical results on the asymptotic behaviour of the solutions to the initial value problem for the Enskog equation when the radius of the gas particles and the Knudsen number tend to zero, that is, respectively, analysis of the asymptotic equivalence with the Boltzmann equation and hydrodynamic limit.

Optimal L 2 -decay of solutions to a cubic dissipative nonlinear Schrödinger equation

2021 ◽  
pp. 1-13
Author(s):  
Kita Naoyasu ◽  
Sato Takuya
Keyword(s):  
Sobolev Space ◽  
Global Solution ◽  
Initial Value Problem ◽  
Trivial Solution ◽  
Decay Estimate ◽  
Weighted Sobolev Space ◽  
The Other ◽  
Initial Value ◽  
Decay Of Solutions ◽  
Dissipative Nonlinearity

This paper presents the optimality of decay estimate of solutions to the initial value problem of 1D Schrödinger equations containing a long-range dissipative nonlinearity, i.e., λ | u | 2 u. Our aim is to obtain the two results. One asserts that, if the L 2 -norm of a global solution, with an initial datum in the weighted Sobolev space, decays at the rate more rapid than ( log t ) − 1 / 2 , then it must be a trivial solution. The other asserts that there exists a solution decaying just at the rate of ( log t ) − 1 / 2 in L 2 .

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