Well/ill-posedness for the dissipative Navier–Stokes system in generalized Carleson measure spaces
As an essential extension of the well known case β∈(12,1]{\beta\kern-1.0pt\in\kern-1.0pt({\frac{1}{2}},1]} to the hyper-dissipative case β∈(1,∞){\beta\kern-1.0pt\in\kern-1.0pt(1,\infty)}, this paper establishes both well-posedness and ill-posedness (not only norm inflation but also indifferentiabili...
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| Format: | Article |
| Language: | English |
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De Gruyter
2017-01-01
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| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2016-0042 |
| _version_ | 1818715949885292544 |
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| author | Wang Yuzhao Xiao Jie |
| author_facet | Wang Yuzhao Xiao Jie |
| author_sort | Wang Yuzhao |
| collection | DOAJ |
| description | As an essential extension of the well known case β∈(12,1]{\beta\kern-1.0pt\in\kern-1.0pt({\frac{1}{2}},1]} to the hyper-dissipative case β∈(1,∞){\beta\kern-1.0pt\in\kern-1.0pt(1,\infty)}, this paper establishes both well-posedness and ill-posedness (not only norm inflation but also indifferentiability of the solution map) for the mild solutions of the incompressible Navier–Stokes system with dissipation (-Δ)12<β<∞{(-\Delta)^{{\frac{1}{2}}<\beta<\infty}} through the generalized Carleson measure spaces of initial data that unify many diverse spaces, including the Q space (Q-s=-α)n{(Q_{-s=-\alpha})^{n}}, the BMO-Sobolev space ((-Δ)-s2BMO)n{((-\Delta)^{-{\frac{s}{2}}}\mathrm{BMO})^{n}}, the Lip-Sobolev space ((-Δ)-s2Lipα)n{((-\Delta)^{-{\frac{s}{2}}}\mathrm{Lip}\alpha)^{n}}, and the Besov space (B˙∞,∞s)n{(\dot{B}^{s}_{\infty,\infty})^{n}}. |
| first_indexed | 2024-12-17T19:11:30Z |
| format | Article |
| id | doaj.art-f044bb4a5b494ab6b49e77d7be1b5b68 |
| institution | Directory Open Access Journal |
| issn | 2191-9496 2191-950X |
| language | English |
| last_indexed | 2024-12-17T19:11:30Z |
| publishDate | 2017-01-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj.art-f044bb4a5b494ab6b49e77d7be1b5b682022-12-21T21:35:52ZengDe GruyterAdvances in Nonlinear Analysis2191-94962191-950X2017-01-018120322410.1515/anona-2016-0042anona-2016-0042Well/ill-posedness for the dissipative Navier–Stokes system in generalized Carleson measure spacesWang Yuzhao0Xiao Jie1Department of Mathematics and Physics, North China Electric Power University, Beijing102206, P. R. China; and School of Mathematics, The University of Edinburgh, Edinburgh, EH9 3FD, United KingdomDepartment of Mathematics and Statistics, Memorial University, St. John’s, NL A1C 5S7, CanadaAs an essential extension of the well known case β∈(12,1]{\beta\kern-1.0pt\in\kern-1.0pt({\frac{1}{2}},1]} to the hyper-dissipative case β∈(1,∞){\beta\kern-1.0pt\in\kern-1.0pt(1,\infty)}, this paper establishes both well-posedness and ill-posedness (not only norm inflation but also indifferentiability of the solution map) for the mild solutions of the incompressible Navier–Stokes system with dissipation (-Δ)12<β<∞{(-\Delta)^{{\frac{1}{2}}<\beta<\infty}} through the generalized Carleson measure spaces of initial data that unify many diverse spaces, including the Q space (Q-s=-α)n{(Q_{-s=-\alpha})^{n}}, the BMO-Sobolev space ((-Δ)-s2BMO)n{((-\Delta)^{-{\frac{s}{2}}}\mathrm{BMO})^{n}}, the Lip-Sobolev space ((-Δ)-s2Lipα)n{((-\Delta)^{-{\frac{s}{2}}}\mathrm{Lip}\alpha)^{n}}, and the Besov space (B˙∞,∞s)n{(\dot{B}^{s}_{\infty,\infty})^{n}}.https://doi.org/10.1515/anona-2016-0042incompressible navier–stokes system with dissipationwell/ill-posedness for mild solutionsgeneralized carleson measure spaces30h25 31c15 35q30 42b37 46e35 |
| spellingShingle | Wang Yuzhao Xiao Jie Well/ill-posedness for the dissipative Navier–Stokes system in generalized Carleson measure spaces Advances in Nonlinear Analysis incompressible navier–stokes system with dissipation well/ill-posedness for mild solutions generalized carleson measure spaces 30h25 31c15 35q30 42b37 46e35 |
| title | Well/ill-posedness for the dissipative Navier–Stokes system in generalized Carleson measure spaces |
| title_full | Well/ill-posedness for the dissipative Navier–Stokes system in generalized Carleson measure spaces |
| title_fullStr | Well/ill-posedness for the dissipative Navier–Stokes system in generalized Carleson measure spaces |
| title_full_unstemmed | Well/ill-posedness for the dissipative Navier–Stokes system in generalized Carleson measure spaces |
| title_short | Well/ill-posedness for the dissipative Navier–Stokes system in generalized Carleson measure spaces |
| title_sort | well ill posedness for the dissipative navier stokes system in generalized carleson measure spaces |
| topic | incompressible navier–stokes system with dissipation well/ill-posedness for mild solutions generalized carleson measure spaces 30h25 31c15 35q30 42b37 46e35 |
| url | https://doi.org/10.1515/anona-2016-0042 |
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