From the 1 of 5 linked papers with an AI index.
5 papers
A clarification on the distinction between nonlocal error and profile residual error in a computer-assisted proof of 3D Euler singularity
Jiajie Chen, Thomas Y. Hou
In \cite{zhang2025dimension}, the author discusses the applicability of a nonexistence result for self-similar profiles to the Hou--Luo scenario and raises questions about the appr…
Analytic finite-rank corrections for singularly weighted estimates in a computer-assisted proof of 3D Euler singularity
Jiajie Chen, Thomas Y. Hou
The paper presents an analytic low‑rank correction technique that enforces required vanishing conditions in singularly weighted energy estimates used in computer‑assisted proofs of…
Asymptotically Self-Similar Blowup for 3D Incompressible Euler with Velocity II: 3D Profiles, Blowup, and Limiting behavior
Jiajie Chen
For any , we construct exact self-similar blowup profiles for the vorticity of the 3D incompressible Euler equation without swirl, and build on them to prove…
Asymptotically Self-Similar Blowup for 3D Incompressible Euler with Velocity I: 1D Limiting Profiles
Jiajie Chen
We consider a one-parameter family of 1D models for the 3D axisymmetric incompressible Euler equation with vorticity and without swirl near the symmetry axis. For $α= \frac…
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…