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We prove the large time existence of solutions to the magnetohydrodynamics equations with slip boundary conditions in a cylindrical domain. Assuming smallness of the L₂-norms of the derivatives of the initial velocity and of the magnetic field with respect to the variable along the axis of the cylinder, we are able to obtain an estimate for the velocity and the magnetic field in without restriction on their magnitude. Then the existence follows from the Leray-Schauder fixed point theorem.
To a domain with conical points Ω, we associate a natural C*-algebra that is motivated by the study of boundary value problems on Ω, especially using the method of layer potentials. In two dimensions, we allow Ω to be a domain with ramified cracks. We construct an explicit groupoid associated to ∂Ω and use the theory of pseudodifferential operators on groupoids and its representations to obtain our layer potentials C*-algebra. We study its structure, compute the associated K-groups, and prove Fredholm...
Le théorème classique de Riesz-Raikov assure que, pour tout entier et toute de , où , les moyennespour presque tout point de . J.Bourgain (cf.Israël Math. Conf. Proc. 1990) a prouvé que la convergence précédente a lieu pour tout réel algébrique et toute de . Dans cet article nous prouvons que, si est un endomorphisme de algébrique sur , dont les valeurs propres sont toutes de module , alors pour toute de , les moyennes convergent vers pour presque tout point de . Nous...
These lectures will focus on those properties of maximal monotone operators which are valid in arbitrary real Banach spaces.
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