IMA Postdoc Seminar (January 26, 2010)

Speaker: Chan, Chi Hin (IMA)

Title: Eventual regularization of the slightly supercritical fractional Burgers equation.

Abstract: In this talk, we present a piece of joint work of Chi Hin Chan, Magdalena Czubak, and Luis Silvestre, in which we established the eventual regularization of solutions to slightly supercritical fractional Burgers equation.

However, we have to point out that, due to the recent work of Kiselev, Nazarov, and Shterenberg, and also that of Alibaud, Droniou, and Vovelle, it is known that shocks can occur to solutions of supercritical fractional Burgers equation. But we show that the shocks will disappear for solutions to slightly supercritical fractional Burgers equation if we wait for a certain period of time T.