Dirichlet and neumann exterior problems for the n-dimensional laplace operator an approach in weighted sobolev spaces

Amrouche, Chérif; Girault, Vivette; Giroire, J.

doi:10.1016/s0021-7824(97)89945-x

Cited by 142 publications

(136 citation statements)

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“…The existence of solutions of this problem under the given conditions has been established in [6]. However, we believe that the inequality (3.12), which does not contain the L 2 -norm of div π, is new.…”

Section: Preliminary Resultsmentioning

confidence: 90%

On the local existence of the free-surface Euler equation with surface tension

Ignatova

Kukavica

2016

ASY

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Section: Preliminary Resultsmentioning

confidence: 90%

On the local existence of the free-surface Euler equation with surface tension

Ignatova

Kukavica

2016

ASY

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“…Moreover, the following Hardy inequality holds (see [4]): (Ω). Hence, it also satisfies the usual trace theorems on the boundary ∂Ω, which we recall, is at least Lipschitz-continuous.…”

Section: Functional Setting and Preliminary Resultsmentioning

confidence: 99%

On the Oseen Problem in Three-Dimensional Exterior Domains

Amrouche

Razafison

2006

Anal. Appl.

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“…This section is dedicated to recalling some results stated in [4,1,2], about the well-posedness of Neumann boundary value problems. We write the problem in the generic form:…”

Section: A Neumann Boundary Value Problemmentioning

confidence: 99%

Locomotion of Articulated Bodies in an Ideal Fluid: 2d Model With Buoyancy, Circulation and Collisions

Munnier

Pinçon

2010

Math. Models Methods Appl. Sci.

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Articulated solid bodies are shape-changing bodies made of rigid solids linked together by means of holonomic constraints prescribed as functions of time. In this paper we study the locomotion of such swimming devices in an ideal fluid. Our study ranges over a wide class of problems: any number of immersed bodies are involved (without being hydrodynamically decoupled), the system fluid-bodies can be partially of totally confined and circulation, buoyancy and collisions between bodies are taken into account. We determine the Euler-Lagrange equation governing the dynamic of the system, study its well-posedness and describe a numerical scheme used in a Matlab toolbox (Biohydrodynamics Toolbox) that has been designed to realize easily related numerical simulations.

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Dirichlet and neumann exterior problems for the n-dimensional laplace operator an approach in weighted sobolev spaces

Cited by 142 publications

References 19 publications

On the local existence of the free-surface Euler equation with surface tension

On the local existence of the free-surface Euler equation with surface tension

On the Oseen Problem in Three-Dimensional Exterior Domains

Locomotion of Articulated Bodies in an Ideal Fluid: 2d Model With Buoyancy, Circulation and Collisions

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