We consider the Cauchy problem for the three-dimensional Navier-Stokes equations, and provide an optimal regularity criterion in terms of and , which are the third components of the velocity and vorticity, respectively. This gives an affirmative answer to an open problem in the paper by P. Penel, M. Pokorný (2004).
We consider the flow of a class of incompressible fluids which are constitutively defined by the symmetric part of the velocity gradient being a function, which can be non-monotone, of the deviator of the stress tensor. These models are generalizations of the stress power-law models introduced and studied by J. Málek, V. Průša, K. R. Rajagopal: Generalizations of the Navier-Stokes fluid from a new perspective. Int. J. Eng. Sci. 48 (2010), 1907–1924. We discuss a potential application of the new...
Nous exposons dans cet article l'analogue de ces résultats d'existence pour l'équation de Navier-Stokes [Cannone (4), Cannone et Planchon (27, 5, 28)], mais sur un domaine extérieur Ωε, complémentaire d'un compact à bord lisse. Les deux difficultés nouvelles qui se présentent sont l'absence d'une représentation explicite en Fourier du semi-groupe associé à l'opérateur de Stokes et la nécessité de transposer la notion d'espace de Besov homogène.
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.
We consider the stationary Stokes system with slip boundary conditions in a bounded domain. Assuming that data functions belong to weighted Sobolev spaces with weights equal to some power of the distance to some distinguished axis, we prove the existence of solutions to the problem in appropriate weighted Sobolev spaces.
We study the nonstationary Navier-Stokes equations in the entire three-dimensional space and give some criteria on certain components of gradient of the velocity which ensure its global-in-time smoothness.
We review the developments of the regularity criteria for the Navier-Stokes equations, and make some further improvements.
In questa nota, si presentano risultati di esistenza e di unicità di misure invarianti per l'equazione di Navier-Stokes che governa il moto di un fluido viscoso incomprimibile omogeneo in un dominio bidimensionale soggetto a una forzante che ha due componenti: una deterministica e una di tipo rumore bianco nella variabile temporale.
In this paper we are concerned with the steady Boussinesq system with mixed boundary conditions. The boundary conditions for fluid may include Tresca slip, leak, one-sided leak, velocity, vorticity, pressure and stress conditions together and the conditions for temperature may include Dirichlet, Neumann and Robin conditions together. For the problem involving the static pressure and stress boundary conditions, it is proved that if the data of the problem are small enough, then there exists a solution...