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Scale Dependence of Contact Line Computations

O. Weinstein, L. M. Pismen (2008)

Mathematical Modelling of Natural Phenomena

The shape and velocity of a sliding droplet are computed by solving the Navier-Stokes equation with free interface boundary conditions. The Galerkin finite element method is implemented in a 2D computation domain discretized using an unstructured mesh with triangular elements. The mesh is refined recursively at the corners (contact points). The stationary sliding velocity is found to be strongly dependent on grid refinement, which is a consequence of the contact line singularity resolved through...

Self-similar solutions in weak Lp-spaces of the Navier-Stokes equations.

Oscar A. Barraza (1996)

Revista Matemática Iberoamericana

The most important result stated in this paper is a theorem on the existence of global solutions for the Navier-Stokes equations in Rn when the initial velocity belongs to the space weak Ln(Rn) with a sufficiently small norm. Furthermore, this fact leads us to obtain self-similar solutions if the initial velocity is, besides, an homogeneous function of degree -1. Partial uniqueness is also discussed.

Smoothness of the motion of a rigid body immersed in an incompressible perfect fluid

Olivier Glass, Franck Sueur, Takéo Takahashi (2012)

Annales scientifiques de l'École Normale Supérieure

We consider the motion of a rigid body immersed in an incompressible perfect fluid which occupies a three-dimensional bounded domain. For such a system the Cauchy problem is well-posed locally in time if the initial velocity of the fluid is in the Hölder space C 1 , r . In this paper we prove that the smoothness of the motion of the rigid body may be only limited by the smoothness of the boundaries (of the body and of the domain). In particular for analytic boundaries the motion of the rigid body is analytic...

Solutions faibles pour des problèmes d’interaction fluide-structure

Benoît Desjardins, Maria J. Esteban (1999/2000)

Séminaire Équations aux dérivées partielles

Nous présentons dans cette note une nouvelle façon d’aborder les questions d’existence de solutions faibles pour certains problèmes d’interaction fluide-structure. Dans l’état actuel, cette approche permet de traiter le cas de solides rigides ou très faiblement déformables, immergés dans un fluide visqueux incompressible ou dans un fluide visqueux compressible dont l’évolution est isentropique.

Solvability of two stationary free boundary problems for the Navier-Stokes equations

V. A. Solonnikov (1998)

Bollettino dell'Unione Matematica Italiana

Si studiano due problemi con frontiera libera per equazioni stazionarie di Navier-Stokes: il problema del movimento di un liquido viscoso incomprimibile generato dalla rotazione di una sbarra rigida immersa nel liquido con velocità angolare assegnata e il problema della fuoriuscita di un liquido da un tubo circolare nello spazio libero. Si assegna l'angolo di contatto tra la frontiera libera e la superficie del tubo e, nel secondo problema, il flusso totale del liquido attraverso l'apertura del...

Some application of the implicit function theorem to the stationary Navier-Stokes equations

Konstanty Holly (1991)

Annales Polonici Mathematici

We prove that - in the case of typical external forces - the set of stationary solutions of the Navier-Stokes equations is the limit of the (full) sequence of sets of solutions of the appropriate Galerkin equations, in the sense of the Hausdorff metric (for every inner approximation of the space of velocities). Then the uniqueness of the N-S equations is equivalent to the uniqueness of almost every of these Galerkin equations.

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