Recent Advances Concerning the Navier-Stokes and Euler Equations

Abstract: In this talk I will discuss some recent progress concerning the Navier-Stokes and Euler equations of incompressible fluid. In particular, issues concerning the lack of uniqueness using the convex integration machinery and their physical relevance. Moreover, I will show the universality of the critical $1/3$ H\"older exponent, conjectured by Onsager for the preservation of energy in Euler equations, by extending the Onsager conjecture for the preservation of generalized entropy in general conservation laws. In addition, I will present a blow-up criterion for the 3D Euler equations based on a class of inviscid regularization for these equations and the effect of physical boundaries on the potential formation of singularity.

analysis of PDEs

Audience: researchers in the topic

Rio de Janeiro webinar on analysis and partial differential equations

Series comments: Talks are held twice a month; start time and day of the week may vary, according to the speaker time zone. A link to join each webinar will be made available in due time here and at sites.google.com/view/webinarpde/home