CMX Student/Postdoc Seminar

Blowup of the 3D Euler/ Navier-Stokes equation remains one of the most challenging and important problems in PDE. We will illustrate the study of self-similar blowups by various 1D models that capture the essential features and mechanism of the Euler equation. We reduce the blowup analysis to the stability analysis of the profile equation. Approximate profile needs to be constructed, either analytically or numerically; and then stability analysis can be established in weighted L^2 or L^\infty norm. Finally, we discuss the implications of the results to the 3D equations, where many of the insights in the results of the models actually corroborates with recent numerical findings of the 3D equations.