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Self-Similar Solutions to the Compressible Euler Equation and their Instabilities
PDE and Applied Math Seminar| Speaker: | Anxo Biasi, Institute of Theoretical Physics, Jagiellonian University |
| Location: | Zoom |
| Start time: | Thu, Apr 22 2021, 1:10PM |
The abrupt implosion of an ideal gas is a process that can be described by a family of self-similar solutions to the compressible Euler equation found by G. Guderely in 1942. Despite this problem received significant attention it was not until 2019 that the existence of smooth solutions was proved. Nevertheless, the construction of these solutions and their stability remained open. In this talk I will describe recent work where we give solution to these problems; we have constructed smooth solutions, studied their stability and explored endpoints of unstable directions.