STEADY FLOWS OF VISCOUS COMPRESSIBLE FLUIDS IN EXTERIOR DOMAINS UNDER SMALL PERTURBATIONS OF GREAT POTENTIAL FORCES

1993 ◽  
Vol 03 (06) ◽  
pp. 725-757 ◽  
Author(s):  
ANTONÍN NOVOTNÝ
Keyword(s):  
Existence And Uniqueness ◽  
Compressible Flows ◽  
Three Dimensional ◽  
Compressible Fluids ◽  
Steady Flows ◽  
Exterior Domains ◽  
Uniqueness Of Solutions ◽  
Small Perturbations ◽  
Zero Velocity ◽  
Potential Forces

We investigate the steady compressible flows in three-dimensional exterior domains, in R3 and [Formula: see text], under the action of small perturbations of large potential forces and zero velocity at infinity. We prove existence and uniqueness of solutions in L2-spaces, and study their regularity as well as the decay at infinity.

scholarly journals The Navier–Stokes regularity problem

2020 ◽  
Vol 378 (2174) ◽  
pp. 20190526
Author(s):  
James C. Robinson
Keyword(s):  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Regularity Of Solutions ◽  
Navier Stokes ◽  
Initial Condition ◽  
Theme Issue ◽  
Uniqueness Of Solutions ◽  
Rigorous Results ◽  
Navier Stokes Equations

There is currently no proof guaranteeing that, given a smooth initial condition, the three-dimensional Navier–Stokes equations have a unique solution that exists for all positive times. This paper reviews the key rigorous results concerning the existence and uniqueness of solutions for this model. In particular, the link between the regularity of solutions and their uniqueness is highlighted. This article is part of the theme issue ‘Stokes at 200 (Part 1)’.

THREE-DIMENSIONAL EXTERIOR PROBLEM OF DARWIN MODEL AND ITS NUMERICAL COMPUTATION

2008 ◽  
Vol 18 (10) ◽  
pp. 1673-1701 ◽  
Author(s):  
NENGSHENG FANG ◽  
LUNG-AN YING
Keyword(s):  
Boundary Value Problem ◽  
Numerical Computation ◽  
Existence And Uniqueness ◽  
Three Dimensional ◽  
Decomposition Theorem ◽  
Exterior Problem ◽  
Exterior Domains ◽  
Numerical Examples ◽  
Infinite Element Method ◽  
Variational Formulations

Darwin model is a good approximation to Maxwell's equations, and this paper is concerned with the boundary value problem of the Darwin model in three-dimensional exterior domains. Firstly we establish the variational formulations of Darwin model in exterior domains and prove the existence and uniqueness. Then we prove a useful decomposition theorem that any function in unbounded exterior domains belonging to L2(Ω) can be decomposed into the sum of a function's gradient and another function's rotation, such decomposition is crucial in inducing the Darwin model. At last we spend some energy in using the infinite element method to solve the Darwin model in axis-symmetric exterior domains cases. Error estimates are obtained in weighted spaces, and numerical examples verify the convergence once again.

scholarly journals On the existence and uniqueness of solutions to stochastic three-dimensional Lagrangian averaged Navier–Stokes equations

2005 ◽  
Vol 462 (2066) ◽  
pp. 459-479 ◽  
Author(s):  
Tomás Caraballo ◽  
José Real ◽  
Takeshi Taniguchi
Keyword(s):  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Uniqueness Of Solutions ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Stochastic Version ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

We prove the existence and uniqueness of solutions for a stochastic version of the three-dimensional Lagrangian averaged Navier–Stokes equation in a bounded domain. To this end, we previously prove some existence and uniqueness results for an abstract stochastic equation and justify that our model falls within this framework.

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.

The mathematics of varistors

2016 ◽  
Vol 28 (2) ◽  
pp. 208-220 ◽  
Author(s):  
GIOVANNI CIMATTI
Keyword(s):  
Boundary Value Problem ◽  
Electric Conductivity ◽  
Electric Potential ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Three Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Uniqueness Of Solutions ◽  
Inversion Theorem

A three-dimensional model of the varistor device is proposed. The thermal and electric conductivity of the material are taken to depend, in addition to the electric potential, on the temperature. Two theorems of existence and uniqueness of solutions for the boundary-value problem which determine the potential and the temperature inside the device are proposed. Levy–Caccioppoli global inversion theorem is used for the proof.

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