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The far-field modelling of transonic compressible flows

C. A. Coclici, Ivan L. Sofronov, Wolfgang L. Wendland (2001)

Mathematica Bohemica

We present a method for the construction of artificial far-field boundary conditions for two- and three-dimensional exterior compressible viscous flows in aerodynamics. Since at some distance to the surrounded body (e.g. aeroplane, wing section, etc.) the convective forces are strongly dominant over the viscous ones, the viscosity effects are neglected there and the flow is assumed to be inviscid. Accordingly, we consider two different model zones leading to a decomposition of the original flow...

The inviscid limit for density-dependent incompressible fluids

Raphaël Danchin (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

This paper is devoted to the study of smooth flows of density-dependent fluids in ℝ N or in the torus 𝕋 N . We aim at extending several classical results for the standard Euler or Navier-Stokes equations, to this new framework.Existence and uniqueness is stated on a time interval independent of the viscosity μ when μ goes to 0 . A blow-up criterion involving the norm of vorticity in L 1 ( 0 , T ; L ∞ ) is also proved. Besides, we show that if the density-dependent Euler equations have a smooth solution on a given time...

The mathematical theory of low Mach number flows

Steven Schochet (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The mathematical theory of the passage from compressible to incompressible fluid flow is reviewed.

The minimum entropy principle for compressible fluid flows in a nozzle with discontinuous cross-section

Dietmar Kröner, Philippe G. LeFloch, Mai-Duc Thanh (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the Euler equations for compressible fluids in a nozzle whose cross-section is variable and may contain discontinuities. We view these equations as a hyperbolic system in nonconservative form and investigate weak solutions in the sense of Dal Maso, LeFloch and Murat [J. Math. Pures Appl.74 (1995) 483–548]. Observing that the entropy equality has a fully conservative form, we derive a minimum entropy principle satisfied by entropy solutions. We then establish the stability of a class...

The problem of data assimilation for soil water movement

François-Xavier Le Dimet, Victor Petrovich Shutyaev, Jiafeng Wang, Mu Mu (2004)

ESAIM: Control, Optimisation and Calculus of Variations

The soil water movement model governed by the initial-boundary value problem for a quasilinear 1-D parabolic equation with nonlinear coefficients is considered. The generalized statement of the problem is formulated. The solvability of the problem is proved in a certain class of functional spaces. The data assimilation problem for this model is analysed. The numerical results are presented.

The problem of data assimilation for soil water movement

François-Xavier Le Dimet, Victor Petrovich Shutyaev, Jiafeng Wang, Mu Mu (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The soil water movement model governed by the initial-boundary value problem for a quasilinear 1-D parabolic equation with nonlinear coefficients is considered. The generalized statement of the problem is formulated. The solvability of the problem is proved in a certain class of functional spaces. The data assimilation problem for this model is analysed. The numerical results are presented.

The quasineutral limit problem in semiconductors sciences

Ling Hsiao (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The mathematical analysis on various mathematical models arisen in semiconductor science has attracted a lot of attention in both applied mathematics and semiconductor physics. It is important to understand the relations between the various models which are different kind of nonlinear system of P.D.Es. The emphasis of this paper is on the relation between the drift-diffusion model and the diffusion equation. This is given by a quasineutral limit from the DD model to the diffusion equation.

The scalar Oseen operator - Δ + ∂ / ∂ x 1 in ℝ 2

Chérif Amrouche, Hamid Bouzit (2008)

Applications of Mathematics

This paper solves the scalar Oseen equation, a linearized form of the Navier-Stokes equation. Because the fundamental solution has anisotropic properties, the problem is set in a Sobolev space with isotropic and anisotropic weights. We establish some existence results and regularities in L p theory.

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