Blowup Criteria for 3D Navier-Stokes Equation: the Vector Potential as a Possible Blowup Criterion
Koji Ohkitani
School of Mathematics and Statistics, University of Sheffield
Date and time:
Friday, October 30, 2015 - 3:00pm
Location:
ECCR 245
Abstract:
We consider basic regularity issues of the Navier-Stokes equations, which is potentially relevant to the problem of turbulence. We review some of the known results obtained so far, centering around the blowup criteria, especially those in terms of critical L3 or H1/2 norms.
We then ask whether the vector potential in 3D serves as a blowup criterion, which is supposed to generalise the L3 criterion. We also ask whether the stream function in 2D serves as a blowup criterion. (In 2D, global regularity is known.) Preliminary results are given in those directions.
Finally, we compare the problem of the Navier-Stokes equations with that of the Burgers equations, the latter of which is linearisable by the Cole-Hopf transform. We introduce a similar transform to the 2D Navier-Stokes equations, which does not lead to linearisation as expected. Rather, we show that the residual term is related to the blowup criterion in terms of velocity.