Displaying similar documents to “The fundamental k -form and global relations.”

Convergence of the rotating fluids system in a domain with rough boundaries

David Gérard-Varet (2003)

Journées équations aux dérivées partielles

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We consider a rotating fluid in a domain with rough horizontal boundaries. The Rossby number, kinematic viscosity and roughness are supposed of characteristic size ϵ . We prove a convergence theorem on solutions of Navier-Stokes Coriolis equations, as ϵ goes to zero, in the well prepared case. We show in particular that the limit system is a two-dimensional Euler equation with a nonlinear damping term due to boundary layers. We thus generalize the results obtained on flat boundaries with...

Finite differences and boundary element methods for non-stationary viscous incompressible flow

Werner Varnhorn (1994)

Banach Center Publications

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We consider an implicit fractional step procedure for the time discretization of the non-stationary Stokes equations in smoothly bounded domains of ℝ³. We prove optimal convergence properties uniformly in time in a scale of Sobolev spaces, under a certain regularity of the solution. We develop a representation for the solution of the discretized equations in the form of potentials and the uniquely determined solution of some system of boundary integral equations. For the numerical computation...

Existence and stability theorems for abstract parabolic equations, and some of their applications

Gerhard Ströhmer, Wojciech Zajączkowski (1996)

Banach Center Publications

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For a class of semi-abstract evolution equations for sections on vector bundles on a three-dimensional compact manifold we prove that for initial values with certain symmetries strong solutions exist for all times. In case these solutions become small after some time, strong solutions exist also for small perturbations of these initial values. Many systems from fluid mechanics are included in this class.

Uniqueness results for some PDEs

Nader Masmoudi (2003)

Journées équations aux dérivées partielles

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Existence of solutions to many kinds of PDEs can be proved by using a fixed point argument or an iterative argument in some Banach space. This usually yields uniqueness in the same Banach space where the fixed point is performed. We give here two methods to prove uniqueness in a more natural class. The first one is based on proving some estimates in a less regular space. The second one is based on a duality argument. In this paper, we present some results obtained in collaboration with...