L. Escauriaza, G. A. Seregin, V. Šverak, “<nobr>$L_{3,\infty}$</nobr>-solutions of the Navier–Stokes equations and backward uniqueness”, Uspekhi Mat. Nauk, 2003, Volume 58, Issue 2(350),Pages <nobr>3–44</nobr>

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Uspekhi Mat. Nauk, 2003 Volume 58, Issue 2(350), Pages 3–44 (Mi rm609)

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$L_{3,\infty}$-solutions of the Navier–Stokes equations and backward uniqueness

L. Escauriaza^a, G. A. Seregin^b, V. Šverak^c

^a Universidad del Pais Vasco-Euskal Herriko Unibertsitatea, Dipartimento di Matematicas
^b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
^c University of Minnesota, School of Mathematics

Abstract: It is shown that the $L_{3,\infty}$-solutions of the Cauchy problem for the three-dimensional Navier–Stokes equations are smooth.

UDC: 517.9

MSC: Primary 35Q30; Secondary 35B65, 35D10, 35A05, 35K05, 35K60, 35B60, 76D05

Received: 15.02.2003

DOI: 10.4213/rm609

English version: Russian Mathematical Surveys, 2003, 58:2, 211–250

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