Local existence and uniqueness of strong solutions to 3-D stochastic Navier-Stokes equations

1997 ◽  
Vol 4 (2) ◽  
pp. 185-200 ◽  
Author(s):  
Marek Capiński ◽  
Szymon Peszat
Keyword(s):  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Local Existence ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Local Existence And Uniqueness

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 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.

Unique Strong Solutions and V -Attractors of a Three Dimensional System of Globally Modified Navier-Stokes Equations

2006 ◽  
Vol 6 (3) ◽  
Author(s):  
Tomás Caraballo ◽  
José Real ◽  
Peter E. Kloeden
Keyword(s):  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Dimensional System ◽  
Navier Stokes Equations ◽  
Three Dimensional System

AbstractWe prove the existence and uniqueness of strong solutions of a three dimensional system of globally modified Navier-Stokes equations. The flattening property is used to establish the existence of global V -attractors and a limiting argument is then used to obtain the existence of bounded entire weak solutions of the three dimensional Navier-Stokes equations with time independent forcing.

Addendum to the Paper “Unique Strong Solutions and V -Attractors of a Three Dimensional System of Globally Modified Navier-Stokes Equations″, Advanced Nonlinear Studies 6 (2006), 411-436

2010 ◽  
Vol 10 (1) ◽  
Author(s):  
Tomás Caraballo ◽  
José Real ◽  
Peter E. Kloeden
Keyword(s):  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Dimensional System ◽  
Uniqueness Of Solutions ◽  
Navier Stokes Equations ◽  
Three Dimensional System

AbstractIn this paper we improve Theorem 7 in [1] which deals with the existence and uniqueness of solutions of the three dimensional globally modified Navier-Stokes equations.

scholarly journals EXISTENCE AND UNIQUENESS OF STRONG SOLUTIONS FOR A COMPRESSIBLE MULTIPHASE NAVIER–STOKES MISCIBLE FLUID-FLOW PROBLEM IN DIMENSION n = 1

2009 ◽  
Vol 19 (03) ◽  
pp. 443-476 ◽  
Author(s):  
C. MICHOSKI ◽  
A. VASSEUR
Keyword(s):  
Diffusion Coefficient ◽  
Fluid Flow ◽  
Existence And Uniqueness ◽  
Flow Problem ◽  
Stokes Equations ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Global Existence And Uniqueness ◽  
Miscible Fluid

We prove the global existence and uniqueness of strong solutions for a compressible multifluid described by the barotropic Navier–Stokes equations in dim = 1. The result holds when the diffusion coefficient depends on the pressure. It relies on a global control in time of the L2 norm of the space derivative of the density, via a new kind of entropy.

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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