A remark on the partial regularity of a suitable weak solution to the Navier-Stokes Cauchy problem

Francesca Crispo; Paolo Maremonti

doi:10.3934/dcds.2017053

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2017, Volume 37, Issue 3: 1283-1294. Doi: 10.3934/dcds.2017053

This issue Previous Article A note on the convergence of the solution of the high order Camassa-Holm equation to the entropy ones of a scalar conservation law Next Article Modified energy functionals and the NLS approximation

A remark on the partial regularity of a suitable weak solution to the Navier-Stokes Cauchy problem

Francesca Crispo^, and
Paolo Maremonti

Dipartimento di Matematica e Fisica, Seconda Università degli Studi di Napoli, via Vivaldi, 43 -Caserta, I 81100, Italy

* Corresponding author: P. Maremonti
* Corresponding author: P. Maremonti

Received: March 1, 2016

Revised: October 1, 2016

Published online: December 1, 2016

This research was partly supported by GNFM-INdAM, and by MIUR via the PRIN 2012 "Nonlinear Hyperbolic Partial Differential Equations, Dispersive and Transport Equations: Theoretical and Applicative Aspects".

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Abstract

Starting from the partial regularity results for suitable weak solutions to the Navier-Stokes Cauchy problem by Caffarelli, Kohn and Nirenberg [1], as a corollary, under suitable assumptions of local character on the initial data, we investigate the behavior in time of the $L_{loc}^\infty$-norm of the solution in a neighborhood of $t=0$. The behavior is the same as for the resolvent operator associated to the Stokes operator.

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Mathematics Subject Classification: Primary:35Q30, 35B65;Secondary:76D03.

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References

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