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Partial Differential Equations & Applied Math: "THE NAVIER-STOKES EQUATIONS: STATIONARY EXISTENCE, CONDITIONAL REGULARITY, AND SELF-SIMILAR SINGULARITIES”

Dr. Nguyen Cong Phuc, Louisiana State University

Friday, November 3, 2017
  1:10–2 p.m.


Location: Surge Building 268
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Category: Seminar

Description:

Both stationary and time-dependent Navier-Stokes equations are discussed. The common theme is that the quadratic nonlinearity and the pressure are both treated as weights generally belonging to a Sobolev space of negative order. In one direction, we obtain the unique existence of solutions to stationary Navier-Stokes equations with small singular external forces that belong to a critical space. The stability of the so-obtained stationary solutions is also discussed. In another direction, some new local energy bounds are obtained for the time-dependent Navier-Stokes equations. As a consequence, several improvements of the known regularity criteria and sharper bounds on the size of the singular sets are obtained. The analysis also allows us to rule out the existence of Leray's backward self-similar solutions to the Navier-Stokes equations with certain low integrability profiles.


This talk is based on joint work with Tuoc Van Phan and Cristi Guevara.


 



Additional Information: Math Seminars

Open to: General Public
Admission: Free
Sponsor: Mathematics

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