Time: 14:00-15:00, Tuesday, October 22 2024

Venue: E4-233, Yungu Campus

Zoom ID: 921 4545 5993

Passcode: 610639

Speaker: Taichi Eguchi, Waseda University

Title: Energy equality and inviscid limit of the fractional Navier-Stokes equations

Abstract: We find a new criterion for the validity of the energy equality of the 3D fractional Navier-Stokes equations in the framework of the Lorentz-Besov spaces. Note that our sufficient condition is strictly weaker than that of Cheskidov et.al. (2008) related to the largest class $L^3(0, T; B^{1/3}_{3,∞})$ for the validity of the energy conservation law of the Euler equations. Moreover, taking the inviscid limit of the fractional Navier-Stokes equations, we obtain the energy conservation law of the Euler equations in the framework of the same Lorentz-Besov spaces. Furthermore, we mention the relation between our new criterion and the Onsager conjecture.