Formation of Point Shocks for 3D Compressible Euler

We consider the 3D isentropic compressible Euler equations with ideal gas law. provide a constructive proof of formation first point shock from smooth initial datum finite energy, no vacuum regions, nontrivial vorticity present at shock, and under symmetry assumptions. prove that for an open set Sobolev-class data are small L∞ perturbation constant state, there exist solutions to which form generic stable in time. The blowup time location can be explicitly computed, except single point, where they cusp-type Hölder C1/3 regularity. Our is based on use modulated self-similar variables used enforce number constraints profile, necessary establish global existence asymptotic stability variables. © 2022 Wiley Periodicals LLC.