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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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 |
| Summary: | 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}}. |
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| ISSN: | 2191-9496 2191-950X |