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Weighted L p-estimates for Stokes flow in ℝ n+ with applications to the non-stationary Navier-Stokes flow

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Abstract

We study the time-decay properties of weighted norms of solutions to the Stokes equations and the Navier-Stokes equations in the half-space ℝ n+ (n ⩾ 2). Three kinds of the weighted L p − L r estimates are established for the Stokes semigroup generated by the Stokes operator in the half-space ℝ n+ (n ⩾ 2). As an application of the weighted estimates of the Stokes semigroup, a class of local and global strong solutions in weighted L p (ℝ n+ ) are constructed, following the approach given by Kato.

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Authors and Affiliations

  1. Division of Mathematics, Department of Mathematical and Physical Sciences, National Natural Science Foundation of China, Beijing, 100085, China

    Cheng He

  2. Department of Mathematics and Center for Nonlinear Studies, Northwest University, Xi’an, 710069, China

    LiZhen Wang

Authors
  1. Cheng He
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  2. LiZhen Wang
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Correspondence to Cheng He.

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He, C., Wang, L. Weighted L p-estimates for Stokes flow in ℝ n+ with applications to the non-stationary Navier-Stokes flow. Sci. China Math. 54, 573–586 (2011). https://doi.org/10.1007/s11425-010-4117-1

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  • DOI: https://doi.org/10.1007/s11425-010-4117-1

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