8 papers
On rotated backwards self-similar solutions of the incompressible 3D Navier-Stokes equations
Ben Pineau, Vlad Vicol
We consider backwards globally self-similar solutions of the 3D incompressible Navier-Stokes equations which are invariant under the joint action of scaling (the natural parabolic…
A new class of Euler explosions
Jiajie Chen, Giorgio Cialdea, Steve Shkoller +1
We study the global-in-time continuation, past the singularity, of the smooth, non-isentropic, radially symmetric imploding solutions of the compressible Euler equations recently c…
Smooth and stable Euler implosions
Jiajie Chen, Steve Shkoller, Vlad Vicol
We construct a new class of self-similar implosion profiles for the multi-dimensional compressible Euler equations. These profiles are smooth, genuinely non-isentropic, radially/sp…
On putative self-similarity for incompressible 3D Euler
Peter Constantin, Mihaela Ignatova, Vlad Vicol
We consider hypothetical solutions of 3D Euler which blow up in finite time in a self-similar fashion. We prove that if the initial data has finite kinetic energy, then the similar…
Finite time singularities in the Landau equation with very hard potentials
Jacob Bedrossian, Jiajie Chen, Maria Pia Gualdani +3
We consider the inhomogeneous Landau equation with and construct smooth, strictly positive initial data that develop a finite time singularity. The -norm…
Classical Euler flows generate the strong Guderley imploding shock wave
Giorgio Cialdea, Steve Shkoller, Vlad Vicol
We prove that Guderley's self-similar imploding shock solution for the compressible Euler equations with ideal--gas law () arises from classical, radially symmetric, shock--f…