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Come for the Burger's, Stay for a New Shock(ing) Result
Student-Run Analysis & PDE| Speaker: | K.R. Chickering, UC Davis |
| Related Webpage: | https://www.math.ucdavis.edu/~krc/ |
| Location: | (Online) Zoom |
| Start time: | Thu, Apr 29 2021, 1:10PM |
We discuss recent work on fractal Burger's equation, a toy model for fluid equations in the supercritical viscosity regime. In particular we prove that stable shocks form in finite time for this model. But before you're scared away...
...we assume only a glancing familiarity with elementary undergraduate PDE concepts; a knowledge of calculus should be plenty. Oh, and we will use the Fourier transform a couple of times.
We will focus on fundamental ideas and shy away from technicalities. We will cover the basic ideas underlying shock formation in Burger's equation and explore how to generalize 'viscosity'. Next we present our result, and give a bird's eye view of the philosophical strategy a group of three aspiring grad students might use to prove such a result.
Our proof follows the cutting edge techniques applied by Buckmaster, Shkoller, and Vicol to a range of fluid problems. These ideas are new, powerful, and FUN!
Joint work with R.C. Moreno-Vasquez and G. Pandya.