CAMS Colloquium: On well-posedness at critical regularity for a family of active scalar equations arising in hydrodynamics

Monday, October 18 at 3:30pm to 4:30pm

This is a past event.
Virtual Event


Vincent Martinez, CUNY

Abstract: This talk discusses a family of active scalar transport equations characterized by increasingly singular constitutive laws. This family includes the 2D Euler and surface quasi-geostrophic (SQG) equations as members, and extrapolates beyond them. Although local well-posedness of the initial value problem in sufficiently regular settings are classical results for both the Euler and SQG equations, ill-posedness at critical regularity has only recently been established. For this talk, we consider various regularizations of this family in its most singular range that recover well-posedness results at the threshold regularity level, in spite of the apparent strongly quasilinear structure of the equations in this regime. This is joint work with M.S. Jolly and A. Kumar.

 

Dial-In Information

Zoom Meeting: https://usc.zoom.us/j/94728448929?pwd=QVpGN0UveENVZXBPNzBVc0lvNktrZz09
Meeting ID: 947 2844 8929
Passcode: 196455

and CAMS Colloquium chat room:

https://usc.zoom.us/j/93724420445?pwd=eENVMTROZlI2eEhucFdzdjZLN0pwdz09
Meeting ID: 937 2442 0445
Passcode: 019455

Event Type

Lecture / Talk / Workshop

Department
Mathematics
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