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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| Published in | Annali dell'Università di Ferrara. Sezione 7. Scienze matematiche Vol. 69; no. 1; pp. 245 - 262 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Milan
Springer Milan
01.05.2023
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0430-3202 1827-1510 |
| DOI | 10.1007/s11565-022-00421-w |
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| Abstract | 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. |
|---|---|
| AbstractList | The initial boundary problem of the Stokes system in the 3D halfspace is considered. The boundary condition subject on x3=0 is that the stress vanishes. Under the condition that the initial value is in L2∩L1 we derive the rate of decay in time of L2 norm of solutions to this problem. 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. |
| Author | Nishida, Takaaki Teramoto, Yoshiaki |
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| Cites_doi | 10.1002/cpa.3160340305 10.1007/BF01457017 10.1007/BF01566609 |
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| Copyright | The Author(s) under exclusive license to Università degli Studi di Ferrara 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| References | Borchers, Miyakawa (CR3) 1988; 282 CR4 Solonnikov (CR6) 1978; 10 Solonnikov (CR5) 1964; 70 Beale (CR1) 1981; 34 Beale, Nishida, Teramoto (CR2) 2020; B82 JT Beale (421_CR1) 1981; 34 W Borchers (421_CR3) 1988; 282 VA Solonnikov (421_CR5) 1964; 70 421_CR4 JT Beale (421_CR2) 2020; B82 VA Solonnikov (421_CR6) 1978; 10 |
| References_xml | – ident: CR4 – volume: 34 start-page: 359 year: 1981 end-page: 392 ident: CR1 article-title: The initial value problem for the Navier-Stokes equations with a free surface publication-title: Comm. Pure Appl. Math. doi: 10.1002/cpa.3160340305 – volume: 282 start-page: 139 year: 1988 end-page: 155 ident: CR3 article-title: decay for the Nvier-Stokes flow in Halfspaces publication-title: Math. Ann. doi: 10.1007/BF01457017 – volume: 70 start-page: 213 year: 1964 end-page: 317 ident: CR5 article-title: Estimates of the solutions of the nonstationary linearized system of Navier-Stokes equations publication-title: Tr. Mat. Inst. Akad. Nauk SSSR – volume: 10 start-page: 336 year: 1978 end-page: 393 ident: CR6 article-title: Estimates of solutions of an initial- and boundary-value problem for the linear nonstationary Navier-Stokes systems publication-title: J. Sov. Math. doi: 10.1007/BF01566609 – volume: B82 start-page: 137 year: 2020 end-page: 157 ident: CR2 article-title: Decay of solutions of the Stokes system arising in free surface flow on an infinite layer publication-title: RIMS Kôkyûroku Bessatsu – volume: 70 start-page: 213 year: 1964 ident: 421_CR5 publication-title: Tr. Mat. Inst. Akad. Nauk SSSR – volume: 10 start-page: 336 year: 1978 ident: 421_CR6 publication-title: J. Sov. Math. doi: 10.1007/BF01566609 – volume: B82 start-page: 137 year: 2020 ident: 421_CR2 publication-title: RIMS Kôkyûroku Bessatsu – ident: 421_CR4 – volume: 282 start-page: 139 year: 1988 ident: 421_CR3 publication-title: Math. Ann. doi: 10.1007/BF01457017 – volume: 34 start-page: 359 year: 1981 ident: 421_CR1 publication-title: Comm. Pure Appl. Math. doi: 10.1002/cpa.3160340305 |
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| Snippet | 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.... The initial boundary problem of the Stokes system in the 3D halfspace is considered. The boundary condition subject on x3=0 is that the stress vanishes. Under... |
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| SubjectTerms | Algebraic Geometry Analysis Boundary conditions Boundary value problems Decay rate Geometry History of Mathematical Sciences Mathematics Mathematics and Statistics Numerical Analysis |
| Title | Decay of solutions to the initial boundary value problem of the stokes system in the halfspace |
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