scholarly journals Strong solutions in the dynamical theory of compressible fluid mixtures

2015 ◽  
Vol 25 (07) ◽  
pp. 1217-1256 ◽  
Author(s):  
Matthias Kotschote ◽  
Rico Zacher
Keyword(s):  
Local Existence ◽  
Strong Solutions ◽  
Dynamical Theory ◽  
Uniqueness Result ◽  
Navier Stokes ◽  
Mixing Ratio ◽  
Strongly Coupled ◽  
Transition Layers ◽  
Fluid Mixtures ◽  
Local Existence And Uniqueness

In this paper we investigate the compressible Navier–Stokes–Cahn–Hilliard equations (the so-called NSCH model) derived by Lowengrub and Truskinovsky. This model describes the flow of a binary compressible mixture; the fluids are supposed to be macroscopically immiscible, but partial mixing is permitted leading to narrow transition layers. The internal structure and macroscopic dynamics of these layers are induced by a Cahn–Hilliard law that the mixing ratio satisfies. The PDE constitute a strongly coupled hyperbolic–parabolic system. We establish a local existence and uniqueness result for strong solutions.

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 Local Existence of Strong Solutions of a Fluid–Structure Interaction Model

2020 ◽  
Vol 22 (4) ◽  
Author(s):  
Sourav Mitra
Keyword(s):  
Stokes Equations ◽  
Local Existence ◽  
Interaction Model ◽  
Strong Solutions ◽  
Coupled System ◽  
Elastic Structure ◽  
Navier Stokes ◽  
Beam Equation ◽  
Navier Stokes Equations ◽  
System Coupling

AbstractWe are interested in studying a system coupling the compressible Navier–Stokes equations with an elastic structure located at the boundary of the fluid domain. Initially the fluid domain is rectangular and the beam is located on the upper side of the rectangle. The elastic structure is modeled by an Euler–Bernoulli damped beam equation. We prove the local in time existence of strong solutions for that coupled system.

GENESIS OF A SOURCE/SINK LINE INTO A SINGULAR UPDRAFT

1998 ◽  
Vol 08 (03) ◽  
pp. 431-444 ◽  
Author(s):  
JOËL CHASKALOVIC
Keyword(s):  
Mathematical Models ◽  
Existence And Uniqueness ◽  
Vortex Line ◽  
Stokes Equations ◽  
Local Existence ◽  
Fluid Motion ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Local Existence And Uniqueness ◽  
Source Sink

Mathematical models applied to tornadoes describe these kinds of flows as an axisymmetric fluid motion which is restricted for not developing a source or a sink near the vortex line. Here, we propose the genesis of a family of a source/sink line into a singular updraft which can modeled one of the step of the genesis of a tornado. This model consists of a three-parameter family of fluid motions, satisfying the steady and incompressible Navier–Stokes equations, which vanish at the ground. We establish the local existence and uniqueness for these fields, at the neighborhood of a nonrotating singular updraft.

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.

APPEARANCE OF A SOURCE/SINK LINE INTO A SWIRLING VORTEX

2003 ◽  
Vol 13 (01) ◽  
pp. 121-142 ◽  
Author(s):  
J. CHASKALOVIC ◽  
A. CHAUVIÈRE
Keyword(s):  
Vortex Line ◽  
Stokes Equations ◽  
Local Existence ◽  
Fluid Motion ◽  
Vertical Shear ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Mature Phase ◽  
Local Existence And Uniqueness ◽  
Source Sink

Several mathematical models applied to tornadoes consist of exact and axisymmetric solutions of the steady and incompressible Navier–Stokes equations. These models studied by Serrin,9 Goldshtik and Shtern8 describe families of fluid motions vanishing at the ground and are restricted not to develop a source nor a sink near the vortex line. Therefore, Serrin showed that the flow patterns of the resulting velocity field may have some realistic characteristics to model the mature phase of the lifetime of a tornado, in comparison with atmospheric observations. On the other hand, no reason has been given to motivate the restriction of the absence of a source/sink vortex line. Therefore, we present here the construction and the analysis of a fluid motion driven by the vertical shear near the ground, the rate of the azimuthal rotation and by the intensity of a central source/sink line. We prove the local existence and uniqueness of a family of fluid motions, leading to the genesis of such source/sink lines inside a non-rotating updraft which does not develop, before perturbation, a source nor a sink.

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