scholarly journals Local strong solutions of the nonhomogeneous Navier-Stokes system with control of the interval ofexistence

2015 ◽  
pp. 1
Author(s):  
Hermann Sohr ◽  
Werner Varnhorn ◽  
Reinhard Farwig
Keyword(s):  
Stokes System ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Local Strong Solutions

scholarly journals Regularity Criteria for a Coupled Navier-Stokes and Q-Tensor System

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Jishan Fan ◽  
Tohru Ozawa
Keyword(s):  
Liquid Crystal ◽  
Nematic Liquid Crystal ◽  
Stokes System ◽  
Type System ◽  
Parabolic Type ◽  
Strong Solutions ◽  
Regularity Criteria ◽  
Navier Stokes ◽  
Liquid Crystal Flow ◽  
Local Strong Solutions

We study a system describing the evolution of a nematic liquid crystal flow. The system couples a forced Navier-Stokes system describing the flow with a parabolic-type system describing the evolution of the nematic crystal director fields (Q-tensors). We prove some regularity criteria for the local strong solutions. However, we do not provide estimates on the rates of increase of high norms.

Strong solutions to the density-dependent incompressible Cahn–Hilliard–Navier–Stokes system

2019 ◽  
Vol 16 (04) ◽  
pp. 701-742 ◽  
Author(s):  
Xiaopeng Zhao
Keyword(s):  
Stokes System ◽  
Initial Density ◽  
Local Existence ◽  
Strong Solutions ◽  
Incompressible Fluids ◽  
Navier Stokes ◽  
Initial Value ◽  
Two Phase ◽  
Density Dependent ◽  
Local Existence And Uniqueness

We study the density-dependent incompressible Cahn–Hilliard–Navier–Stokes system, which describes a two-phase flow of two incompressible fluids with different densities. We establish the local existence and uniqueness of strong solutions to the initial value problem in a bounded domain, when the initial density function enjoys a positive lower bound.

scholarly journals Robustness of strong solutions to the compressible Navier-Stokes system

2014 ◽  
Vol 362 (1-2) ◽  
pp. 281-303 ◽  
Author(s):  
Peter Bella ◽  
Eduard Feireisl ◽  
Bum Ja Jin ◽  
Antonín Novotný
Keyword(s):  
Stokes System ◽  
Strong Solutions ◽  
Navier Stokes

scholarly journals Local existence of strong solutions and weak–strong uniqueness for the compressible Navier–Stokes system on moving domains

2019 ◽  
Vol 150 (5) ◽  
pp. 2255-2300 ◽  
Author(s):  
Ondřej Kreml ◽  
Šárka Nečasová ◽  
Tomasz Piasecki
Keyword(s):  
Boundary Conditions ◽  
Stokes System ◽  
Local Existence ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Strong Uniqueness ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Moving Domains ◽  
Open Question

AbstractWe consider the compressible Navier–Stokes system on time-dependent domains with prescribed motion of the boundary. For both the no-slip boundary conditions as well as slip boundary conditions we prove local-in-time existence of strong solutions. These results are obtained using a transformation of the problem to a fixed domain and an existence theorem for Navier–Stokes like systems with lower order terms and perturbed boundary conditions. We also show the weak–strong uniqueness principle for slip boundary conditions which remained so far open question.

BLOW-UP CRITERIA FOR THE NAVIER–STOKES EQUATIONS OF COMPRESSIBLE FLUIDS

2008 ◽  
Vol 05 (01) ◽  
pp. 167-185 ◽  
Author(s):  
JISHAN FAN ◽  
SONG JIANG
Keyword(s):  
Blow Up ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Compressible Fluids ◽  
Navier Stokes ◽  
Positive Density ◽  
Heat Conducting ◽  
Navier Stokes Equations ◽  
Local Strong Solutions

We study the Navier–Stokes equations of three-dimensional compressible isentropic and two-dimensional heat-conducting flows in a domain Ω with nonnegative density, which may vanish in an open subset (vacuum) of Ω, and with positive density, respectively. We prove some blow-up criteria for the local strong solutions.

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