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Spatial and temporal decay estimate of the Stokes flow of weighted [formula omitted]initial data in the half space

Authors
Journal
Nonlinear Analysis Theory Methods & Applications
0362-546X
Publisher
Elsevier
Publication Date
Volume
73
Issue
5
Identifiers
DOI: 10.1016/j.na.2010.04.076
Keywords
  • Stokes
  • Half Space
  • Spatial
  • Temporal
  • Decay Rate

Abstract

Abstract In this paper, we derive the spatial and temporal decay estimate of the Stokes solution e − t A a in the half space when the prescribed initial data is in a weighted L 1 space. We obtained that ‖ x i r e − t A a ‖ L ∞ ≤ C t − n 2 − 1 2 ‖ x i r x n a ‖ L 1 + C t − n 2 + r − 1 2 ‖ x n a ‖ L 1 for 0 ≤ r < n if i = n and 0 ≤ r < n − 1 if i = 1 , … , n − 1 .

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