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On the \(L^p\)\(L^q\) estimates of the gradient of solutions to the Stokes problem

  • Paolo MaremontiEmail author
Article

Abstract

This paper is concerned with estimates of the gradient of the solutions to the Stokes IBVP both in a bounded and in an exterior domain. More precisely, we look for estimates of the kind \(||\nabla v(t)||_q \le g(t)||\nabla v_0||_p,\;q\ge p>1,\) for all \(t>0\), where function g is independent of v.

Keywords

Stokes problem Semigroup properties 

Mathematics Subject Classification

35B45 35Q30 76D07 

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Notes

Acknowledgements

The author is grateful to some anonymous referees for the careful reading of the paper. The referee’s comments have made the paper more readable.

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Authors and Affiliations

  1. 1.Dipartimento di Matematica e FisicaUniversità degli Studi della Campania “L. Vanvitelli”CasertaItaly

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