Global well-posedness to the Cauchy problem of 2D density-dependent micropolar equations with large initial data and vacuum

2020 ◽  
Vol 491 (1) ◽  
pp. 124294
Author(s):  
Yang Liu
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Well Posedness ◽  
Large Initial Data ◽  
Density Dependent ◽  
The Cauchy Problem

scholarly journals Global well-posedness to the Cauchy problem of 2D inhomogeneous incompressible magnetic Bénard equations with large initial data and vacuum

2021 ◽  
Vol 6 (11) ◽  
pp. 12085-12103
Author(s):  
Zhongying Liu ◽  
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Initial Density ◽  
Well Posedness ◽  
Far Field ◽  
Large Initial Data ◽  
Global Strong Solution ◽  
Vacuum States ◽  
The Cauchy Problem ◽  
Field Decay

<abstract><p>In this paper, we are concerned with the Cauchy problem of inhomogeneous incompressible magnetic Bénard equations with vacuum as far-field density in $ \Bbb R^2 $. We prove that if the initial density and magnetic field decay not too slowly at infinity, the system admits a unique global strong solution. Note that the initial data can be arbitrarily large and the initial density can contain vacuum states and even has compact support. Moreover, we extend the result of [16, 17] to the global one.</p></abstract>

BLOW-UP OF THE SOLUTION FOR SEMILINEAR DAMPED WAVE EQUATION WITH TIME-DEPENDENT DAMPING

2012 ◽  
Vol 14 (05) ◽  
pp. 1250034
Author(s):  
JIAYUN LIN ◽  
JIAN ZHAI
Keyword(s):  
Cauchy Problem ◽  
Wave Equation ◽  
Initial Data ◽  
Upper Bound ◽  
Blow Up ◽  
Time Dependent ◽  
Damped Wave Equation ◽  
Large Initial Data ◽  
Power Type ◽  
The Cauchy Problem

We consider the Cauchy problem for the damped wave equation with time-dependent damping and a power-type nonlinearity |u|ρ. For some large initial data, we will show that the solution to the damped wave equation will blow up within a finite time. Moreover, we can show the upper bound of the life-span of the solution.

scholarly journals Global Analysis for Rough Solutions to the Davey-Stewartson System

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Han Yang ◽  
Xiaoming Fan ◽  
Shihui Zhu
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Nonlinear Equation ◽  
Global Solution ◽  
Global Analysis ◽  
Space Time ◽  
Well Posedness ◽  
The Cauchy Problem ◽  
New Space ◽  
Time Bounds

The global well-posedness of rough solutions to the Cauchy problem for the Davey-Stewartson system is obtained. It reads that if the initial data is inHswiths> 2/5, then there exists a global solution in time, and theHsnorm of the solution obeys polynomial-in-time bounds. The new ingredient in this paper is an interaction Morawetz estimate, which generates a new space-timeLt,x4estimate for nonlinear equation with the relatively general defocusing power nonlinearity.

Weak solutions to a hydrodynamic model for semiconductors: the Cauchy problem

1995 ◽  
Vol 125 (1) ◽  
pp. 115-131 ◽  
Author(s):  
Pierangelo Marcati ◽  
Roberto Natalini
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Existence Theorem ◽  
Weak Solutions ◽  
Hydrodynamic Model ◽  
Fractional Step ◽  
Large Initial Data ◽  
Global Weak Solutions ◽  
The Cauchy Problem

We investigate the Cauchy problem for a hydrodynamic model for semiconductors. An existence theorem of global weak solutions with large initial data is obtained by using the fractional step Lax—Friedrichs scheme and Godounov scheme.

Sign in / Sign up

Export Citation Format

Share Document