On the Lp-Lq maximal regularity of the Neumann problem for the Stokes equations in a bounded domain
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Yoshihiro Shibata
and
Senjo Shimizu
Abstract
In this paper, we prove the Lp-Lq 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 V. A. Solonnikov, On the transient motion of an isolated volume of viscous incompressible fluid, Math. USSR Izvest. 31 (1988), 381–405., but he assumed that p = q > 3 and considered only the finite time interval case. In this paper, we consider not only the case: 1 < p, q < ∞ but also the infinite time interval case. Especially, we obtain the Lp-Lq 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.
© Walter de Gruyter
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Articles in the same Issue
- Parabolic equations with BMO nonlinearity in Reifenberg domains
- Castelnuovo theory and the geometric Schottky problem
- Cohomology of rational forms and a vanishing theorem on toric varieties
- On the asymptotic expansion of complete Ricciflat Kähler metrics on quasi-projective manifolds
-
The Chow ring of
- Explicit n-descent on elliptic curves, I. Algebra
- On the Lp-Lq maximal regularity of the Neumann problem for the Stokes equations in a bounded domain
- Parameterized stratification and piece number of D-semianalytic sets
