Strong Solutions to 3D Compressible Navier-Stokes Equations with Two-Directional Short Pulse Initial Data

Christodoulou first introduced Short pulse initial data to show the shock formation for compressible Euler equations and the formation of black holes for Einstein equations. Short pulse initial datum is the one chosen to be supported in the ball of radius delta and with amplitude delta( 1/ 2) which looks like a pulse. By introducing the change of variable, the short pulse type initial data become general initial data. Based on the new observations for the effective viscous flux and new decay estimates for the density via the Lagrangian coordinate, we prove the global well-posedness of solutions to the compressible Navier-Stokes equations with short pulse initial data in two directions which allow the density of the fluid to have large amplitude delta(- alpha/gamma) with delta is an element of (0, 1].