Title: Amplitude Blowup in Radial Euler Flows
Speaker: Charis Tsikkou (West Virginia U.)
Speaker's URL: https://mathanddata.wvu.edu/directory/faculty/charis-tsikkou
Abstract: We show that the full compressible Euler system admits unbounded solutions. The examples are radial flows of similarity type and describe a spherically symmetric and continuous wave moving toward the origin. At time of focusing, the primary flow variables suffer amplitude blowup at the origin. The flow is continued beyond collapse and gives rise to an expanding shock wave. We verify that the resulting flow provides a genuine weak solution to the full, multi-d compressible Euler system. While unbounded radial Euler flows have been known since the work of Guderley (1942), those are at the borderline of the regime covered by the Euler model: the upstream pressure field vanishes identically (either because of vanishing temperature or vanishing density there). In contrast, the solutions we build exhibit an everywhere strictly positive pressure field, demonstrating that the geometric effect of wave focusing is strong enough on its own to generate unbounded values of primary flow variables. This is joint work with Helge Kristian Jenssen (PSU).
URL associated with Seminar: https://research.math.osu.edu/pde/
Zoom Meeting: 948 6539 2210 Password: 314159
