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ON THE INTERACTION BETWEEN QUASILINEAR ELASTODYNAMICS AND THE NAVIERSTOKES EQUATIONS
, 2005
"... Abstract. The interaction between a viscous fluid and an elastic solid is modeled by a system of parabolic and hyperbolic equations, coupled to one another along the moving material interface through the continuity of the velocity and traction vectors. We prove the existence and uniqueness (locally ..."
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in time) of strong solutions in Sobolev spaces for quasilinear elastodynamics coupled to the incompressible NavierStokes equations. Unlike our approach in [5] for the case of linear elastodynamics, we cannot employ a fixedpoint argument on the nonlinear system itself, and are instead forced
NavierStokes Equations
"... The interaction between a viscous fluid and an elastic solid is modeled by a system of parabolic and hyperbolic equations, coupled to one another along the moving material interface through the continuity of the velocity and traction vectors. We prove the existence and uniqueness (locally in time) o ..."
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) of strong solutions in Sobolev spaces for quasilinear elastodynamics coupled to the incompressible NavierStokes equations. Unlike our approach in [5] for the case of linear elastodynamics, we cannot employ a fixedpoint argument on the nonlinear system itself, and are instead forced to regularize it by a
ABSTRACT Title of dissertation: Weakly Compressible NavierStokes Approximation of Gas Dynamics
"... This dissertation addresses mathematical issues regarding weakly compressible approximations of gas dynamics that arise both in fluid dynamical and in kinetic settings. These approximations are derived in regimes in which (1) transport coefficients (viscosity and thermal conductivity) are small and ..."
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while Re maintains order unity, we derive the weakly compressible NavierStokes approximation—a quadratic system. Each of these weakly compressible approximations govern both the acoustic and the incompressible modes of the gas. In the fluid dynamical setting, our derivations begin with the fully
Estimates of optimal accuracy for the BrezziPitkäranta approximation of the NavierStokes problem.
"... Abstract: This paper deals with a singular perturbation of the stationary NavierStokes system. Thereby the term ε2∆p is added to the continuity equation, where ε is small parameter. For sufficiently regular and small data, existence of a unique solution is proved. This solution converges to the cor ..."
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Abstract: This paper deals with a singular perturbation of the stationary NavierStokes system. Thereby the term ε2∆p is added to the continuity equation, where ε is small parameter. For sufficiently regular and small data, existence of a unique solution is proved. This solution converges
Application Of The Method Of Lines To The Compressible NavierStokes Equations
, 2000
"... Introduction One of the basic principles of mathematics is to split complex problems into a number of less complicated ones, which have been already resolved or which are easier to treat. Numerical solution of the compressible NavierStokes equations is such a complex problem. We apply the wellkn ..."
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known Method of lines to the system of partial dierential equations to split its numerical solution into the following partial problems: To approximate the system of partial dierential equations with a system of ordinary dierential equations (ODE's), to analyze the existence and uniqueness
Frequency Domain Formulation Of Linearized NavierStokes Equations
, 1997
"... . A naturally parallelizable formulation is considered for solving linearized timedependent NavierStokes equations. The evolution problem is first converted into a complex valued elliptic system by Fourier transformation. Existence and uniqueness are then given for the resulting problems for each ..."
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Cited by 2 (2 self)
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. A naturally parallelizable formulation is considered for solving linearized timedependent NavierStokes equations. The evolution problem is first converted into a complex valued elliptic system by Fourier transformation. Existence and uniqueness are then given for the resulting problems for each
Global Existence and Uniqueness Theorem for 3DNavier Stokes System on T3 for small initial conditions
 in the spaces Φ (α), arXiv:0710.3842v1, to appear in Pure and Applied Mathematics Quarterly 4, No
"... Dedicated to G.A. Margulis on the occasion of his sixtieth birthday. Abstract:We consider Cauchy problem for threedimensional NavierStokes system with periodic boundary conditions with initial data from the space of pseudomeasures Φ(α). We provide global existence and uniqueness of the solution f ..."
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Cited by 5 (0 self)
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Dedicated to G.A. Margulis on the occasion of his sixtieth birthday. Abstract:We consider Cauchy problem for threedimensional NavierStokes system with periodic boundary conditions with initial data from the space of pseudomeasures Φ(α). We provide global existence and uniqueness of the solution
EXISTENCE AND UNIQUENESS OF SOLUTIONS OF THE BOUSSINESQ SYSTEM WITH NONLINEAR THERMAL DIFFUSION
"... The Boussinesq system of hydrodynamics equations [3], [26] arises from a zero order approximation to the coupling between the Navier–Stokes equations and the thermodynamic equation [25]. Presence of density gradients in a fluid allows the conversion of gravitational potential energy into motion thro ..."
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The Boussinesq system of hydrodynamics equations [3], [26] arises from a zero order approximation to the coupling between the Navier–Stokes equations and the thermodynamic equation [25]. Presence of density gradients in a fluid allows the conversion of gravitational potential energy into motion
A regularity result for a solidfluid system associated to the compressible NavierStokes equations
 Ann. Inst. H. Poincaré Anal. Non Linéaire
"... Abstract In this paper we deal with a fluidstructure interaction problem for a compressible fluid and a rigid structure immersed in a regular bounded domain in dimension 3. The fluid is modelled by the compressible NavierStokes system in the barotropic regime with noslip boundary conditions and ..."
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Cited by 7 (5 self)
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structure rigide évoluant à l'intérieur d'un domaine borné et régulier en dimension 3. Le fluide est décrit par le système de NavierStokes compressible barotrope avec des conditions de nonglissement sur le bord et le mouvement de la structure est régi par les lois de conservation des moments
Existence and uniqueness of solutions to the Boussinesq system with nonlinear thermal diffusion
, 1997
"... The Boussinesq system arises in Fluid Mechanics when motion is governed by density gradients caused by temperature or concentration differences. In the former case, and when thermodynamical coefficients are regarded as temperature dependent, the system consists of the NavierStokes equations and the ..."
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Cited by 7 (1 self)
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of solutions of the general problem as well as the uniqueness of solutions when the spatial dimension is two. 1991 Mathematics Subject Classification: 35K55, 35D05, 35B30, 76R10. Keywords and Phrases: Free convection, existence and uniqueness of solutions. Note: Work partially carried out under project MAS 1.3
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