scholarly journals On Strong Solutions of Regularized Model of a Viscoelastic Medium with Variable Boundary

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Vladimir Orlov
Keyword(s):  
Viscoelastic Medium ◽  
Stokes System ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Systems Of Equations ◽  
Initial Value ◽  
Planar Case ◽  
Variable Boundary ◽  
With Memory ◽  
Regularized Model

We consider the initial-value problem for systems of equations describing the evolution of a viscoelastic medium with variable boundary with memory along the trajectories of a velocity field, which generalizes the Navier-Stokes system of equations. Nonlocal existence and uniqueness theorem of strong solutions containing senior square-integrable derivatives in the planar case are established.

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.

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