Navier–Stokes Cauchy Problem with | v 0 ( x )| 2 Lying in the Kato Class K 3

Francesca Crispo and Paolo Maremonti
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Francesca Crispo: Dipartimento di Matematica e Fisica, Università degli Studi della Campania “L. Vanvitelli”, 81100 Caserta, Italy
Paolo Maremonti: Dipartimento di Matematica e Fisica, Università degli Studi della Campania “L. Vanvitelli”, 81100 Caserta, Italy

Mathematics, 2021, vol. 9, issue 11, 1-14

Abstract: We investigate the 3D Navier–Stokes Cauchy problem. We assume the initial datum v 0 is weakly divergence free, sup R 3 ? R 3 | v 0 ( y ) | 2 | x ? y | d y < ? and | v 0 ( y ) | 2 ? K 3 , where K 3 denotes the Kato class. The existence is local for arbitrary data and global if sup R 3 ? R 3 | v 0 ( y ) | 2 | x ? y | d y is small. Regularity and uniqueness also hold.

Keywords: Navier–Stokes equations; existence; regular solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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