131 research outputs found
On the 3D steady flow of a second grade fluid past an obstacle
We study steady flow of a second grade fluid past an obstacle in three space
dimensions. We prove existence of solution in weighted Lebesgue spaces with
anisotropic weights and thus existence of the wake region behind the obstacle.
We use properties of the fundamental Oseen tensor together with results
achieved in \cite{Koch} and properties of solutions to steady transport
equation to get up to arbitrarily small \ep the same decay as the Oseen
fundamental solution
Very weak solutions and large uniqueness classes of stationary Navier–Stokes equations in bounded domains of R2
AbstractExtending the notion of very weak solutions, developed recently in the three-dimensional case, to bounded domains Ω⊂R2 we obtain a new class of unique solutions u in Lq(Ω), q>2, to the stationary Navier–Stokes system −Δu+u⋅∇u+∇p=f, divu=k, u|∂Ω=g with data f,k,g of low regularity. As a main consequence we obtain a new uniqueness class also for classical weak or strong solutions. Indeed, such a solution is unique if its Lq-norm is sufficiently small or the data satisfy the uniqueness condition of a very weak solution
Global Solution to the Three-Dimensional Incompressible Flow of Liquid Crystals
The equations for the three-dimensional incompressible flow of liquid
crystals are considered in a smooth bounded domain. The existence and
uniqueness of the global strong solution with small initial data are
established. It is also proved that when the strong solution exists, all the
global weak solutions constructed in [16] must be equal to the unique strong
solution
Partial Regularity of solutions to the Four-dimensional Navier-Stokes equations at the first blow-up time
The solutions of incompressible Navier-Stokes equations in four spatial
dimensions are considered. We prove that the two-dimensional Hausdorff measure
of the set of singular points at the first blow-up time is equal to zero.Comment: 19 pages, a comment regarding five or higher dimensional case is
added in Remark 1.3. accepted by Comm. Math. Phy
INTEGRANTES EQUIPO DE EDUCACIÓN VIAL EN MADRID [Material gráfico]
Copia digital. Madrid : Ministerio de Educación, Cultura y Deporte. Subdirección General de Coordinación Bibliotecaria, 201
Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor
In this paper we provide a sufficient condition, in terms of only one of the
nine entries of the gradient tensor, i.e., the Jacobian matrix of the velocity
vector field, for the global regularity of strong solutions to the
three-dimensional Navier-Stokes equations in the whole space, as well as for
the case of periodic boundary conditions
Relative entropies, suitable weak solutions, and weak strong uniqueness for the compressible Navier-Stokes system
We introduce the notion of relative entropy for the weak solutions of the
compressible Navier-Stokes system. We show that any finite energy weak solution
satisfies a relative entropy inequality for any pair of sufficiently smooth
test functions. As a corollary we establish weak-strong uniqueness principle
for the compressible Navier-Stokes system
Integral potential method for a transmission problem with Lipschitz interface in R^3 for the Stokes and Darcy–Forchheimer–Brinkman PDE systems
The purpose of this paper is to obtain existence and uniqueness results in weighted Sobolev spaces for transmission problems for the non-linear Darcy-Forchheimer-Brinkman system and the linear Stokes system in two complementary Lipschitz domains in R3, one of them is a bounded Lipschitz domain with connected boundary, and the other one is the exterior Lipschitz domain R3 n. We exploit a layer potential method for the Stokes and Brinkman systems combined with a fixed point theorem in order to show the desired existence and uniqueness results, whenever the given data are suitably small in some weighted Sobolev spaces and boundary Sobolev spaces
A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra
Transmission Problems for the Navier–Stokes and Darcy–Forchheimer–Brinkman Systems in Lipschitz Domains on Compact Riemannian Manifolds
M. Kohr acknowledges the support of the Grant PN-II-ID-PCE-2011-3-0994 of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI. The research has been also partially supported by the Grant EP/M013545/1: “Mathematical Analysis of Boundary-Domain Integral Equations for Nonlinear PDEs” from the EPSRC, UK
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