On the global existence and time decay estimates in critical spaces for the Navier-Stokes-Poisson system

2017 ◽  
Vol 290 (13) ◽  
pp. 1939-1970 ◽  
Author(s):  
Noboru Chikami ◽  
Raphaël Danchin
Keyword(s):  
Global Existence ◽  
Navier Stokes ◽  
Decay Estimates ◽  
Time Decay ◽  
Poisson System ◽  
Critical Spaces

SOME ASYMPTOTICS FOR A REACTIVE NAVIER–STOKES–POISSON SYSTEM

1999 ◽  
Vol 09 (07) ◽  
pp. 1039-1076 ◽  
Author(s):  
B. DUCOMET
Keyword(s):  
Global Existence ◽  
Global Solution ◽  
Spherical Model ◽  
Navier Stokes ◽  
Positive Energy ◽  
Stability Of Solutions ◽  
Poisson System ◽  
Rigid Core ◽  
Existence And Stability

We prove global existence and stability of solutions for a spherical model of reactive compressible self-gravitating fluid when a rigid core is present. In the absence of core, we show that no global solution of positive energy can exist.

Asymptotic stability of rarefaction wave for the compressible Navier‐Stokes‐Korteweg equations in the half space

2021 ◽  
pp. 1-24
Author(s):  
Yeping Li ◽  
Jing Tang ◽  
Shengqi Yu
Keyword(s):  
Asymptotic Stability ◽  
Rarefaction Wave ◽  
Half Space ◽  
Compressible Fluid ◽  
Boundary Data ◽  
Initial Perturbation ◽  
Navier Stokes ◽  
Asymptotic State ◽  
Decay Estimates ◽  
Time Decay

In this study, we are concerned with the asymptotic stability towards a rarefaction wave of the solution to an outflow problem for the Navier-Stokes Korteweg equations of a compressible fluid in the half space. We assume that the space-asymptotic states and the boundary data satisfy some conditions so that the time-asymptotic state of this solution is a rarefaction wave. Then we show that the rarefaction wave is non-linearly stable, as time goes to infinity, provided that the strength of the wave is weak and the initial perturbation is small. The proof is mainly based on $L^{2}$ -energy method and some time-decay estimates in $L^{p}$ -norm for the smoothed rarefaction wave.

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.

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