scholarly journals Existence of global strong solution for the compressible Navier-Stokes system and the Korteweg system in two-dimension

2013 ◽  
Vol 20 (2) ◽  
pp. 141-164 ◽  
Author(s):  
Boris Haspot
Keyword(s):  
Strong Solution ◽  
Stokes System ◽  
Navier Stokes ◽  
Two Dimension ◽  
Global Strong Solution

Global strong solution for viscous incompressible heat conducting Navier–Stokes flows with density-dependent viscosity

2018 ◽  
Vol 16 (05) ◽  
pp. 623-647 ◽  
Author(s):  
Xin Zhong
Keyword(s):  
Strong Solution ◽  
Variable Viscosity ◽  
Initial Density ◽  
Energy Estimates ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Stokes Flows ◽  
Global Strong Solution ◽  
Regularity Properties ◽  
Nonhomogeneous Heat

We study an initial boundary value problem for the nonhomogeneous heat conducting fluids with non-negative density. First of all, we show that for the initial density allowing vacuum, the strong solution exists globally if the gradient of viscosity satisfies [Formula: see text]. Then, under certain smallness condition, we prove that there exists a unique global strong solution to the 2D viscous nonhomogeneous heat conducting Navier–Stokes flows with variable viscosity. Our method relies upon the delicate energy estimates and regularity properties of Stokes system and elliptic equation.

scholarly journals Global existence of strong solution for the Cucker–Smale–Navier–Stokes system

2014 ◽  
Vol 257 (6) ◽  
pp. 2225-2255 ◽  
Author(s):  
Hyeong-Ohk Bae ◽  
Young-Pil Choi ◽  
Seung-Yeal Ha ◽  
Moon-Jin Kang
Keyword(s):  
Global Existence ◽  
Strong Solution ◽  
Stokes System ◽  
Navier Stokes

scholarly journals Vanishing viscosity limit for the compressible Navier–Stokes system via measure-valued solutions

2020 ◽  
Vol 27 (6) ◽  
Author(s):  
Danica Basarić
Keyword(s):  
Strong Convergence ◽  
Strong Solution ◽  
Stokes System ◽  
Spatial Domain ◽  
Euler System ◽  
Navier Stokes ◽  
Strong Uniqueness ◽  
Vanishing Viscosity ◽  
Vanishing Viscosity Limit ◽  
Viscosity Limit

AbstractWe identify a class of measure-valued solutions of the barotropic Euler system on a general (unbounded) spatial domain as a vanishing viscosity limit for the compressible Navier–Stokes system. Then we establish the weak (measure-valued)–strong uniqueness principle, and, as a corollary, we obtain strong convergence to the Euler system on the lifespan of the strong solution.

Sign in / Sign up

Export Citation Format

Share Document