scholarly journals Optimal Time-decay Estimates for the Compressible Navier–Stokes Equations in the Critical L p Framework

2016 ◽  
Vol 224 (1) ◽  
pp. 53-90 ◽  
Author(s):  
Raphaël Danchin ◽  
Jiang Xu
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Optimal Time ◽  
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.

Optimal time decay of the compressible Navier–Stokes equations for a reacting mixture

Nonlinearity ◽  
2021 ◽  
Vol 34 (9) ◽  
pp. 5955-5978
Author(s):  
Zefu Feng ◽  
Guangyi Hong ◽  
Changjiang Zhu
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Optimal Time ◽  
Time Decay ◽  
Navier Stokes Equations
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