Global existence and asymptotic behavior for the compressible Navier-Stokes equations with a non-autonomous external force and a heat source

2009 ◽  
Vol 32 (8) ◽  
pp. 1011-1040 ◽  
Author(s):  
Yuming Qin ◽  
Xiaona Yu
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Heat Source ◽  
External Force ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF THE COMPRESSIBLE NAVIER–STOKES EQUATIONS FOR A 1D ISOTHERMAL VISCOUS GAS

2008 ◽  
Vol 18 (08) ◽  
pp. 1383-1408 ◽  
Author(s):  
YUMING QIN ◽  
YANLI ZHAO
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Stokes Equations ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Navier Stokes ◽  
Asymptotic Behavior Of Solutions ◽  
Navier Stokes Equations ◽  
Viscous Gas ◽  
Initial Boundary Value

In this paper, we prove the global existence and asymptotic behavior of solutions in Hi(i = 1, 2) to an initial boundary value problem of a 1D isentropic, isothermal and the compressible viscous gas with an non-autonomous external force in a bounded region.

scholarly journals Global Existence of Cylinder Symmetric Solutions for the Nonlinear Compressible Navier-Stokes Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-18
Author(s):  
Lan Huang ◽  
Fengxiao Zhai ◽  
Beibei Zhang
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Heat Source ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Large Initial Data ◽  
Navier Stokes Equations ◽  
New Ideas ◽  
External Forces

We prove the global existence of cylinder symmetric solutions to the compressible Navier-Stokes equations with external forces and heat source inR3for any large initial data. Some new ideas and more delicate estimates are used to prove this result.

GLOBAL EXISTENCE TO THE NAVIER–STOKES EQUATIONS THROUGH A SELF-SIMILAR-LIKE UPPER SOLUTION

2012 ◽  
Vol 14 (05) ◽  
pp. 1250031
Author(s):  
GUY BERNARD
Keyword(s):  
Global Existence ◽  
Heat Equation ◽  
Initial Velocity ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Dimensional Euclidean Space ◽  
Time Interval ◽  
Navier Stokes Equations ◽  
Upper Solution ◽  
Self Similar

A global existence result is presented for the Navier–Stokes equations filling out all of three-dimensional Euclidean space ℝ3. The initial velocity is required to have a bell-like form. The method of proof is based on symmetry transformations of the Navier–Stokes equations and a specific upper solution to the heat equation in ℝ3× [0, 1]. This upper solution has a self-similar-like form and models the diffusion process of the heat equation. By a symmetry transformation, the problem is transformed into an equivalent one having a very small initial velocity. Using the upper solution, the equivalent problem is then solved in the time interval [0, 1]. This local solution is then extended to the time interval [0, ∞) by an iterative process. At each step, the problem is extended further in time in an interval of time whose length is greater than one, thus producing the global solution. Each extension is transformed, by an appropriate change of variables, into the first local problem in the time interval [0, 1]. These transformations exploit the diffusive and self-similar-like nature of the upper solution.

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