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Nonlinear Analysis

Small scale creation in active scalars

Alexander Kiselev, Duke University

Location:  Zoom
Date & time: Wednesday, 08 December 2021 at 9:30AM - 10:30AM

 Abstract: An active scalar is advected by fluid velocity that is determined by the scalar itself. Active scalars appear in many situations in fluid mechanics, with the most classical example being 2D Euler equation in vorticity form. Other prominent examples are the surface quasi-geostrophic (SQG) equation that comes from atmospheric science and the incompressible porous media (IPM) equation modeling the fluid flow in porous media. Usually, active scalar equations are both nonlinear and nonlocal, and their solutions spontaneously generate small scales. In this talk, I will discuss rigorous examples of small scale formation that involves infinite in time growth of derivatives for the 2D Euler equation, the SQG equation and the 2D IPM equation.

Zoom link:
Meeting ID: 964 3090 5091 Passcode: 491508

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