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# Quantitative regularity theory for the Navier-Stokes equations in critical spaces

### Early Career Math Colloquium

Quantitative regularity theory for the Navier-Stokes equations in critical spaces
Series: Early Career Math Colloquium
Location: Online
Presenter: Stan Palasek, UCLA

Abstract: An important question in the theory of the incompressible Navier-Stokes equations is whether boundedness of the velocity in various norms implies regularity of the solution. Critical norms are conjectured to be (roughly) the threshold between positive and negative answers to this question. Of particular interest are 3D solutions in the critical endpoint space $L_t^\infty L_x^3$ for which Escauriaza-Seregin-Sverak famously proved global regularity. Recently Tao improved upon this result by proving quantitative bounds on the solution and conditions on a hypothetical blowup. In this talk we discuss the quantitative approach to regularity including some sharper results in the axisymmetric case, as well as extensions to other critical spaces and to higher dimensions.

Zoom: Meeting ID: 892 9809 3679  Password: “arizona” (all lower case)