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Nonlinear Analysis

Formation and development of singularities for the compressible Euler equations

Vlad Vicol, Courant Institute, New York University

Location:  Hill Center Room 705
Date & time: Tuesday, 01 November 2022 at 1:40PM - 2:40PM

Abstract: We consider the compressible Euler equations of fluid dynamics, in multiple space dimensions. In this talk, we discuss our program of completely describing the formation and development of stable singularities, from smooth initial conditions. The questions we address are: given smooth initial conditions, precisely how does the first singularity arise? is the mechanism stable? how can one geometrically characterize the preshock (the boundary of the space-time set on which the solution remains smooth)? precisely how does the entropy-producing shock wave instantaneously develop from the preshock? does uniqueness hold once the shock has formed? do other singularities instantaneously arise after the preshock? In this level of detail the problem was previously open even in one space dimension. We discuss a sequence of joint works with Steve Shkoller, Tristan Buckmaster, and Theodore Drivas, in which we have developed a multidimensional theory to answer the above questions.

Seminar website:  Nonlinear Analysis Seminar


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