The Navier-Stokes equations: stationary existence, conditional regularity, and self-similar singularities (Lecture 2)
Speaker |
Prof. Nguyen Cong Phuc,
Louisiana State University, Baton Rouge
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When |
Jul 27, 2017
from 04:00 PM to 05:00 PM |
Where | LH 006 |
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Abstract: In these two lectures, 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.
The first lecture will be mainly on the preliminary background for the Navier-Stokes, whereas the main results will be discussed in the second lecture.
These talks are based on joint work with Tuoc Van Phan and Cristi Guevara.