On stable implosions
On stable implosions
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Vlad Vicol, New York University
Fine Hall 314
We exhibit a new class of self-similar implosion solutions for the full compressible Euler equations. For any value of the adiabatic exponent, we construct a sequence of implosion profiles which are smooth (real analytic before collapse) and have an explicit similarity exponent (a closed-form expression). The first profile in this sequence (the ''ground state'') possesses remarkable stability properties, even outside of spherical symmetry, making it an ideal benchmark for multi-d Euler codes. This is joint work with J. Chen (U Chicago) and S. Shkoller (UC Davis).