Global well-posedness and time-decay estimates for compressible Navier-Stokes equations with reaction diffusion

2020 ◽  
Author(s):  
Wenjun Wang ◽  
Huanyao Wen
Keyword(s):  
Stokes Equations ◽  
Reaction Diffusion ◽  
Navier Stokes ◽  
Well Posedness ◽  
Decay Estimates ◽  
Time Decay ◽  
Navier Stokes Equations

scholarly journals Time-Decay Estimates for Linearized Two-Phase Navier–Stokes Equations with Surface Tension and Gravity

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 761
Author(s):  
Hirokazu Saito
Keyword(s):  
Surface Tension ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Dimensional Euclidean Space ◽  
Decay Estimates ◽  
Time Decay ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Linearized Equations ◽  
Estimates Of Solutions

The aim of this paper is to show time-decay estimates of solutions to linearized two-phase Navier-Stokes equations with surface tension and gravity. The original two-phase Navier-Stokes equations describe the two-phase incompressible viscous flow with a sharp interface that is close to the hyperplane xN=0 in the N-dimensional Euclidean space, N≥2. It is well-known that the Rayleigh–Taylor instability occurs when the upper fluid is heavier than the lower one, while this paper assumes that the lower fluid is heavier than the upper one and proves time-decay estimates of Lp-Lq type for the linearized equations. Our approach is based on solution formulas for a resolvent problem associated with the linearized equations.

scholarly journals Global Well-Posedness and Long Time Decay of Fractional Navier-Stokes Equations in Fourier-Besov Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Weiliang Xiao ◽  
Jiecheng Chen ◽  
Dashan Fan ◽  
Xuhuan Zhou
Keyword(s):  
Besov Spaces ◽  
Critical Case ◽  
Stokes Equations ◽  
Global Solutions ◽  
Navier Stokes ◽  
Well Posedness ◽  
Time Decay ◽  
Navier Stokes Equations ◽  
The Cauchy Problem ◽  
Long Time

We study the Cauchy problem of the fractional Navier-Stokes equations in critical Fourier-Besov spacesFB˙p,q1-2β+3/p′. Some properties of Fourier-Besov spaces have been discussed, and we prove a general global well-posedness result which covers some recent works in classical Navier-Stokes equations. Particularly, our result is suitable for the critical caseβ=1/2. Moreover, we prove the long time decay of the global solutions in Fourier-Besov spaces.

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