PACM Colloquium: Turbulent weak solutions of the Euler equations

Mon, Dec 5, 2016, 4:00 pm

Motivated by Kolmogorov's theory of hydrodynamic turbulence, we consider dissipative weak solutions to the 3D incompressible Euler equations. We show that there exist infinitely many weak solutions of the 3D Euler equations, which are continuous in time, lie in a Sobolev space $H^s$ with respect to space, and they do not conserve the kinetic energy. Here the smoothness parameter $s$ is at the Onsager critical value $1/3$, consistent with Kolmogorov's $-4/5$ law for the third order structure functions. We shall also discuss bounds for the second order structure functions, which deviate from the classical Kolmogorov 1941 theory. This talk is based on joint work with T. Buckmaster and N. Masmoudi. 

Fine Hall 214
Event category: 

Upcoming Events

*Online Conference* Analysis of Fluids and Related Topics: Traveling wave solutions to the free boundary Navier-Stokes equations, Speaker: Ian Tice, Carnegie Mellon University

*Online Seminar* Graduate Student Seminar: Locally Interacting Markov Chains on Random and Heterogeneous Graphs, Speaker, Mira Gordin

VIRTUAL IDeAS Seminar: Yong Sheng Soh, National University of Singapore

Wed, Mar 17, 2021, 10:30 am
Location: via Zoom - Link TBA