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A New Approach to the Regularity ofWeak Lq-Solutions of Stokes and Similar Equations via the Cosserat Operator

In: Advances in Mathematical Fluid Mechanics

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  • Christian G. Simader

    (Universität Bayreuth)

Abstract

Throughout this paper let be a bounded domain with sufficiently smooth boundary. We present a new approach to the problem of higher regularity of weak Lq -solutions to Stokes' equation (Theorem 8), Stokes-like equations (Theorems 9 and 10) and the Lamé-Navier equation (Theorem 11). The key point is a regularity property of the so-called Cosserat operator Zq (see (19)). This can be easily deduced (see Theorem 6) from an estimate due to Weyers. With the help of this regularity result the regularity problem for the equations mentioned above can be reduced to the corresponding results for the Laplacian and the Bilaplacian (see Theorems 1 and 2).

Suggested Citation

  • Christian G. Simader, 2009. "A New Approach to the Regularity ofWeak Lq-Solutions of Stokes and Similar Equations via the Cosserat Operator," Springer Books, in: Rolf Rannacher & Adélia Sequeira (ed.), Advances in Mathematical Fluid Mechanics, pages 553-572, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-04068-9_30
    DOI: 10.1007/978-3-642-04068-9_30
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