L3,∞-solutions of the Navier-Stokes equations and backward uniqueness

By Luis Escauriaza, G A Seregin, Vladimír Sverák. 2003

637 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/951066d55c8e95475d74cfb5f081be717a908b55

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Citations in the corpus

Logarithmically improved regularity criterion for the Boussinesq equations in Besov spaces with negative indices (2016, background): “R 3, while the limit case r = 1 was covered much later by Escauriaza, Seregin and Sverak [20].”
Two regularity criteria for the 3D MHD equations (2009, background): “ty issue has been thoroughly investigated for the 3D Navier-Stokes equations and many important regularity criteria have been established (see, e.g., [3],[4],[5],[6],[8],[9],[10],[12], [14],[15],[20],[21],[25],[29],[30], [31],[32],[37],[41],[42],[44],[46],[53],[54]). Some of these criteria can be ex”
On the Regularity Criterion of Weak Solution for the 3D Viscous Magneto-Hydrodynamics Equations (2007, methodology): “For the 3D Navier-Stokes equations, the Serrin-type criterion states that a Leray-Hopf weak solution u is regular, provided the following condition holds [1, 9 ,11,16,19]:”
On the Regularity Conditions for the Navier-Stokes and Related Equations (2005, positive): “After that there are further developments and refinements by Serrin ([29]), Fabes-Jones-Riviere ([20]), KozonoTaniuchi ([22]), and Escauriaza-Sverak-Seregin ([19]).”
Nonuniqueness of weak solutions to the Navier-Stokes equation (2017, neutral): “These conditions and their generalizations have culminated with the work of Escauriaza-Seregin-Šverák [27] who proved the Lt L 3 x endpoint.”
On the uniqueness of heat flow of harmonic maps and hydrodynamic flow of nematic liquid crystals (2010, methodology): “Next we want to modify the standard argument on the small energy regularity on nonhomogeneous Navier-Stokes equations, see for example [1, 8 , 16, 18, 20].”
On smoothness of L3,∞-solutions to the Navier–Stokes equations up to boundary (2005, methodology): “The main idea how to treat boundary regularity of L3,∞-solutions is similar to the case of interior regularity: reduction to a backward uniqueness problem for the heat operator, see [15], [2], and [4].”
Quantitative bounds for critically bounded solutions to the Navier-Stokes equations (2019, methodology): “As our bounds are quantitative and do not depend on any smooth norms of the solution, it is possible to extend the results here to weaker notions of solution, such as mild solutions of Kato [10], the weak Leray-Hopf solutions studied in [7], or the suitable weak solutions from [4], by using the regu”
Global regularity for some classes of large solutions to the Navier-Stokes equations (2008, neutral): “There are two positive numbers ε 0 and η such that for any divergence free vector ﬁeld v 0 satisfying then, for any positive ε smaller than ε 0 , the initial data generates a global smooth solution of ( NS ) on T 2 × R .”