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

  • * Corresponding author: P. Maremonti

    * Corresponding author: P. Maremonti 
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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  • 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.

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

    Citation:

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    [2] F. Crispo and P. Maremonti, On the spatial asymptotic decay of a suitable weak solution to the Navier-Stokes Cauchy problem, Nonlinearity, 29 (2016), 1355-1383.  doi: 10.1088/0951-7715/29/4/1355.
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