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CMX Student/Postdoc Seminar

Friday, April 28, 2023
4:00pm to 5:00pm
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Annenberg 104
Self-similar blowups of various models in fluid dynamics
Yixuan Wang, G3 Graduate Student, Applied and Computational Mathematics, Caltech,

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.

For more information, please contact Jolene Brink by email at [email protected].