Journal ArticleDOI
A well-posed problem for the exterior Stokes equations in two and three dimensions
TLDR
In this paper, the Stokes problem is treated in exterior Lipschitz continuous domains of ℝ2 andℝ3 using the weighted Sobolev spaces of Hanouzet and Giroire.Abstract:
This paper treats the Stokes problem in exterior Lipschitz-continuous domains of ℝ2 and ℝ3. Using the weighted Sobolev spaces of Hanouzet (in ℝ3) and Giroire (in ℝ2), we establish the inf-sup condition between the velocity and pressure spaces. This fundamental result shows that the variational Stokes problem is well-posed in those spaces. In the last paragraph, we obtain additional regularity of the solution when the data are smoother.read more
Citations
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Book ChapterDOI
On Stokes' Problem
TL;DR: In this paper, the Navier-Stokes problem in bounded and exterior Lipschitz domains with boundary datum in was studied and a very weak solution was shown in bounded domains.
Journal ArticleDOI
Weak solutions for the exterior Stokes problem in weighted Sobolev spaces
Frédéric Alliot,Chérif Amrouche +1 more
TL;DR: In this article, the existence and uniqueness results for the exterior Stokes problem in weighted Sobolev spaces were extended and the regularity of the solutions (u, π) was studied.
Journal ArticleDOI
Variational approach for the Stokes and Navier–Stokes systems with nonsmooth coefficients in Lipschitz domains on compact Riemannian manifolds
Mirela Kohr,Wolfgang L. Wendland +1 more
TL;DR: In this article, Mitrea et al. show well-posedness results for Dirichlet problems for the Stokes and Navier-Stokes systems with variable coefficients in Sobolev spaces in Lipschitz domains on compact Riemannian manifolds.
Journal ArticleDOI
Controllability of 3d low reynolds number swimmers
Jérôme Lohéac,Alexandre Munnier +1 more
TL;DR: In this article, the authors consider a self-deformable body immersed in a fluid, the flow of which is governed by the stationary Stokes equations, and show that any microswimmer has the ability to track, by performing a sequence of shape changes, any given trajectory in the fluid.
Journal ArticleDOI
THE STOKES PROBLEM IN ℝn: AN APPROACH IN WEIGHTED SOBOLEV SPACES
F. Alliot,C. Amrouche +1 more
TL;DR: In this article, the Stokes problem is studied in weighted Sobolev spaces and the density of smooth solenoidal vector fields in the subspace of W √ m,p √ n √ p √ 1,n √ 2 is established for which data the problem has solutions with prescribed decay or growth.
References
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Book
Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms
TL;DR: This paper presents the results of an analysis of the "Stream Function-Vorticity-Pressure" Method for the Stokes Problem in Two Dimensions and its applications to Mixed Approximation and Homogeneous Stokes Equations.
Journal ArticleDOI
On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers
TL;DR: In this paper, the authors describe a fitting for hose end fittings that is suitable for use in conjunction with a cross-linked polyethylene hose or pipe, where a body incorporating a nipple adapted for insertion in a pipe end and a clamping ring normally retained on the body and adapted for clamping action about the outer surface of said pipe end is described.
Journal ArticleDOI
The finite element method with Lagrangian multipliers
TL;DR: In this article, the Dirichlet problem for second order differential equations is chosen as a model problem to show how the finite element method may be implemented to avoid difficulty in fulfilling essential (stable) boundary conditions.