Vol. 7, No. 8, 2014

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Global regularity for a slightly supercritical hyperdissipative Navier–Stokes system

David Barbato, Francesco Morandin and Marco Romito

Vol. 7 (2014), No. 8, 2009–2027
Abstract

We prove global existence of smooth solutions for a slightly supercritical hyperdissipative Navier–Stokes under the optimal condition on the correction to the dissipation. This proves a conjecture formulated by Tao.

Keywords
Navier–Stokes, dyadic model, global existence, slightly supercritical Navier–Stokes equations.
Mathematical Subject Classification 2010
Primary: 76D03, 76D05
Secondary: 35Q30, 35Q35
Milestones
Received: 24 July 2014
Accepted: 14 December 2014
Published: 5 February 2015
Authors
David Barbato
Dipartimento di Matematica
Università di Padova
Via Trieste 63
I-35121 Padova
Italy
Francesco Morandin
Dipartimento di Matematica e Informatica
Università di Parma
Parco Area delle Scienze, 53/A
I-43121 Parma
Italy
Marco Romito
Dipartimento di Matematica
Università di Pisa
Largo Bruno Pontecorvo 5
I-56127 Pisa
Italy