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On the Lp-Lq maximal regularity of the Neumann problem for the Stokes equations in a bounded domain

✍ Scribed by Shibata, Yoshihiro; Shimizu, Senjo

Book ID
118740440
Publisher
Walter de Gruyter GmbH & Co. KG
Year
2008
Tongue
English
Weight
509 KB
Volume
2008
Category
Article
ISSN
0075-4102

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✦ Synopsis

In this paper, we prove the L p -L q maximal regularity of solutions to the Neumann problem for the Stokes equations with non-homogeneous boundary condition and divergence condition in a bounded domain. The result was first stated by Solonnikov [17], but he assumed that p ΒΌ q > 3 and considered only the finite time interval case. In this paper, we consider not only the case: 1 < p; q < y but also the infinite time interval case. Especially, we obtain the L p -L q maximal regularity theorem with exponential stability on the infinite time interval.

Our method can be applied to any initial boundary value problem for the equation of parabolic type with suitable boundary condition which generates an analytic semigroup, for example the Stokes equation with non-slip, slip or Robin boundary conditions.

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