Lower bounds on blowing-up solutions of the three-dimensional Navier-Stokes equations in \(\dot H^{3/2}\), \(\dot H^{5/2}\), and \(\dot B^{5/2}_{2,1}\) (Q2814475)
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scientific article; zbMATH DE number 6596275
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Lower bounds on blowing-up solutions of the three-dimensional Navier-Stokes equations in \(\dot H^{3/2}\), \(\dot H^{5/2}\), and \(\dot B^{5/2}_{2,1}\) |
scientific article; zbMATH DE number 6596275 |
Statements
22 June 2016
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Navier-Stokes equations
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blowup
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Sobolev spaces
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Besov spaces
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commutator estimates
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Lower bounds on blowing-up solutions of the three-dimensional Navier-Stokes equations in \(\dot H^{3/2}\), \(\dot H^{5/2}\), and \(\dot B^{5/2}_{2,1}\) (English)
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The authors derive blowup rates in the Sobolev and Besov spaces norms mentioned in the title of the paper for solutions of the three-dimensional Navier-Stokes system that develop a singularity in a finite time. These are either optimal or strong lower decay estimates. Their proofs involve new inequalities for the nonlinearity which are obtained from the Paley-Littlewood analysis.
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