scholarly journals Corrigendum to “Global well-posedness of strong solutions with large oscillations and vacuum to the compressible Navier-Stokes-Poisson equations subject to large and non-flat doping profile” [J. Differ. Equ., 269(10) (2020) 8468–8508]

2021 ◽  
Author(s):  
Shengquan Liu ◽  
Xinying Xu ◽  
Jianwen Zhang
Keyword(s):  
Strong Solutions ◽  
Doping Profile ◽  
Navier Stokes ◽  
Well Posedness ◽  
Poisson Equations

Global well-posedness of compressible bipolar Navier-Stokes-Poisson equations

2011 ◽  
Vol 28 (5) ◽  
pp. 925-940 ◽  
Author(s):  
Yi Quan Lin ◽  
Cheng Chun Hao ◽  
Hai Liang Li
Keyword(s):  
Navier Stokes ◽  
Well Posedness ◽  
Poisson Equations

scholarly journals Well-posedness analysis of multicomponent incompressible flow models

2021 ◽  
Author(s):  
Dieter Bothe ◽  
Pierre-Etienne Druet
Keyword(s):  
Stokes Equations ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Well Posedness ◽  
Navier Stokes Equations ◽  
Flow Models ◽  
Change Of Variables ◽  
Algebraic Formula ◽  
Time Existence ◽  
Specific Volumes

AbstractIn this paper, we extend our study of mass transport in multicomponent isothermal fluids to the incompressible case. For a mixture, incompressibility is defined as the independence of average volume on pressure, and a weighted sum of the partial mass densities stays constant. In this type of models, the velocity field in the Navier–Stokes equations is not solenoidal and, due to different specific volumes of the species, the pressure remains connected to the densities by algebraic formula. By means of a change of variables in the transport problem, we equivalently reformulate the PDE system as to eliminate positivity and incompressibility constraints affecting the density, and prove two type of results: the local-in-time well-posedness in classes of strong solutions, and the global-in-time existence of solutions for initial data sufficiently close to a smooth equilibrium solution.

scholarly journals Local well-posedness of a quasi-incompressible two-phase flow

2020 ◽  
Author(s):  
Helmut Abels ◽  
Josef Weber
Keyword(s):  
Two Phase Flow ◽  
Type Equation ◽  
Strong Solutions ◽  
Variable Density ◽  
Diffuse Interface ◽  
Navier Stokes ◽  
Well Posedness ◽  
Phase Flow ◽  
Two Phase ◽  
Fluid Mixture

AbstractWe show well-posedness of a diffuse interface model for a two-phase flow of two viscous incompressible fluids with different densities locally in time. The model leads to an inhomogeneous Navier–Stokes/Cahn–Hilliard system with a solenoidal velocity field for the mixture, but a variable density of the fluid mixture in the Navier–Stokes type equation. We prove existence of strong solutions locally in time with the aid of a suitable linearization and a contraction mapping argument. To this end, we show maximal $$L^2$$ L 2 -regularity for the Stokes part of the linearized system and use maximal $$L^p$$ L p -regularity for the linearized Cahn–Hilliard system.

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