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PDEs and Fluid Dynamics

descriptionPublicationkeyboard_double_arrow_right Part of book or chapter of book , Other literature type 01 Jan 2011 Germany English Publisher:Springer Berlin Heidelberg

Authors: Diening, Lars; Harjulehto, Petteri; Hästö, Peter; Růžička, Michael; Diening, Lars; Harjuletho, Petteri; Hästö, Peter; +1 Authors

doi: 10.1007/978-3-642-18363-8_14

PDEs and Fluid Dynamics

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Abstract

We use the theory of Calderon–Zygmund operators to prove regularity results for the Poisson problem and the Stokes problem, to show the solvability of the divergence equation, and to prove Korn’s inequality. These problems belong to the most classical problems treated in the theory of partial differential equations and fluid dynamics. It turns out that the treatment, especially of the whole space problems requires the notion of homogeneous Sobolev spaces, which have been studied in Sect. 12.2. The Poisson problem and the Stokes system are studied in the first two sections. After that we study the divergence equation and its consequences.

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Germany

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