Explicit expression for the fundamental solution to the Cauchy problem for the one-velocity Boltzmann equation in the case of a one-dimensional isotropic medium

1999 ◽  
Vol 97 (4) ◽  
pp. 4368-4389
Author(s):  
Yu. B. Yanushanets
Keyword(s):  
Cauchy Problem ◽  
Boltzmann Equation ◽  
Fundamental Solution ◽  
Explicit Expression ◽  
Isotropic Medium ◽  
One Dimensional ◽  
The Cauchy Problem ◽  
The One

GLOBAL INHOMOGENEOUS SCHRÖDINGER FLOW

2000 ◽  
Vol 11 (08) ◽  
pp. 1079-1114 ◽  
Author(s):  
HONG-YU WANG ◽  
YOU-DE WANG
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Spin System ◽  
Holomorphic Sectional Curvature ◽  
Heisenberg Spin ◽  
One Dimensional ◽  
The Cauchy Problem ◽  
Schrodinger Flow ◽  
The One ◽  
Complete Kähler Manifold

In this paper, we consider the global existence of one-dimensional nonautonomous inhomogeneous Schrödinger flow. By exploiting geometric symmetries, we prove that, given a smooth initial map, the Cauchy problem of the one-dimensional nonautonomous inhomogeneous Schrödinger flow from S1 into a complete Kähler manifold with constant holomorphic sectional curvature admits a unique global smooth solution. As a corollary, we establish the global existence for the Cauchy problem of the inhomogeneous Heisenberg spin system.

scholarly journals On non-resistive limit of 1D MHD equations with no vacuum at infinity

2021 ◽  
Vol 11 (1) ◽  
pp. 702-725
Author(s):  
Zilai Li ◽  
Huaqiao Wang ◽  
Yulin Ye
Keyword(s):  
Cauchy Problem ◽  
A Priori ◽  
Strong Solutions ◽  
Mhd Equations ◽  
Well Posedness ◽  
Large Initial Data ◽  
One Dimensional ◽  
The Cauchy Problem ◽  
Global Strong Solutions ◽  
The One

Abstract In this paper, the Cauchy problem for the one-dimensional compressible isentropic magnetohydrodynamic (MHD) equations with no vacuum at infinity is considered, but the initial vacuum can be permitted inside the region. By deriving a priori ν (resistivity coefficient)-independent estimates, we establish the non-resistive limit of the global strong solutions with large initial data. Moreover, as a by-product, the global well-posedness of strong solutions for the compressible resistive MHD equations is also established.

Global well-posedness of the Cauchy problem for the equations of a one-dimensional viscous heat-conducting gas with Lebesgue initial data

2004 ◽  
Vol 134 (5) ◽  
pp. 939-960 ◽  
Author(s):  
Song Jiang ◽  
Alexander Zlotnik
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Heat Conducting ◽  
Well Posedness ◽  
Global Weak Solutions ◽  
One Dimensional ◽  
Lipschitz Continuous ◽  
Viscous Heat ◽  
The Cauchy Problem ◽  
The One

We study the Cauchy problem for the one-dimensional equations of a viscous heat-conducting gas in the Lagrangian mass coordinates with the initial data in the Lebesgue spaces. We prove the existence, the uniqueness and the Lipschitz continuous dependence on the initial data of global weak solutions.

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