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.

scholarly journals GLOBAL SOLUTION FOR THE GENERALIZED ANISOTROPIC NAVIER–STOKES EQUATIONS WITH LARGE DATA

2015 ◽  
Vol 20 (2) ◽  
pp. 205-231 ◽  
Author(s):  
Daoyuan Fang ◽  
Bin Han
Keyword(s):  
Initial Data ◽  
Besov Space ◽  
Global Solution ◽  
Stokes Equations ◽  
Large Data ◽  
Navier Stokes ◽  
Unique Global Solution ◽  
Large Initial Data ◽  
Navier Stokes Equations ◽  
Anisotropic Besov Space

We are concerned with 3D incompressible generalized anisotropic Navier– Stokes equations with hyperdissipative term in horizontal variables. We prove that there exists a unique global solution for it with large initial data in anisotropic Besov space.

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