Global existence for non-autonomous Navier-Stokes equations with discontinuous initial data

2017 ◽  
Vol 40 (12) ◽  
pp. 4625-4632
Author(s):  
Shenglan Wen ◽  
Qixia Shen ◽  
Lan Huang
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Discontinuous Initial Data

scholarly journals Global Solutions to the Spherically Symmetric Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Discontinuous Initial Data

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Ruxu Lian ◽  
Jianwei Yang ◽  
Jian Liu
Keyword(s):  
Initial Data ◽  
Regular Solution ◽  
Stokes Equations ◽  
Jump Discontinuity ◽  
Navier Stokes ◽  
Spherically Symmetric ◽  
Navier Stokes Equations ◽  
Density Dependent ◽  
Discontinuous Initial Data ◽  
Dependent Viscosity

We consider the initial boundary value problem for the spherically symmetric isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficients and discontinuous initial data in this paper. For piecewise regular initial density with bounded jump discontinuity, we show that there exists a unique global piecewise regular solution. In particular, the jump of density decays exponentially in time and the piecewise regular solution tends to the equilibrium state exponentially ast→+∞.

scholarly journals Global existence and decay estimate of solution to compressible quantum Navier-Stokes equations with damping

2021 ◽  
Author(s):  
Zhonger Wu ◽  
Zhong Tan ◽  
Xu TANG
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Decay Estimate ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Smooth Solutions ◽  
Navier Stokes Equations ◽  
Homogeneous Sobolev Space ◽  
Higher Derivative ◽  
The Cauchy Problem

In this paper, we consider the Cauchy problem of the compressible quantum Navier-Stokes equations with damping in R3. We first assume that the H3-norm of the initial data is sufficiently small while the higher derivative can be arbitrarily large, and prove the global existence of smooth solutions. Then the decay estimate of the solution is derived for the initial data in a homogeneous Sobolev space or Besov space with negative exponent. In addition, the usual Lp−L2(1 ≤ p ≤ 2) type decay rate is obtained without assuming that the Lpnorm of the initial data is sufficiently small.

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