Decay of solutions to the initial boundary value problem of the stokes system in the halfspace

The initial boundary problem of the Stokes system in the 3D halfspace is considered. The boundary condition subject on x 3 = 0 is that the stress vanishes. Under the condition that the initial value is in L 2 ∩ L 1 we derive the rate of decay in time of L 2 norm of solutions to this problem.

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Bibliographic Details
Published inAnnali dell'Università di Ferrara. Sezione 7. Scienze matematiche Vol. 69; no. 1; pp. 245 - 262
Main Authors Nishida, Takaaki, Teramoto, Yoshiaki
Format Journal Article
LanguageEnglish
Published Milan Springer Milan 01.05.2023
Springer Nature B.V
Subjects
Algebraic Geometry
Analysis
Boundary conditions
Boundary value problems
Decay rate
Geometry
History of Mathematical Sciences
Mathematics
Mathematics and Statistics
Numerical Analysis
Stress condition
decay
35Q30
Stokes system
76D07
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ISSN0430-3202
1827-1510
DOI10.1007/s11565-022-00421-w

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Summary:The initial boundary problem of the Stokes system in the 3D halfspace is considered. The boundary condition subject on x 3 = 0 is that the stress vanishes. Under the condition that the initial value is in L 2 ∩ L 1 we derive the rate of decay in time of L 2 norm of solutions to this problem.
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ISSN:0430-3202
1827-1510
DOI:10.1007/s11565-022-00421-w