PDE research follows existence, uniqueness, regularity, and blowup for specified equations and initial data.
4 records · Includes focused interests · How we rate progress
Alpöge and Buckmaster report finite-time blowup for the inviscid Boussinesq equations on R² with smooth spatially compact forcing in both equations. Temperature remains bounded, while its gradient and the vorticity become unbounded.
Read original source Alpöge–Buckmaster manuscript and AI statementcims.nyu.edu
Original report: 2026-09-07The manuscript reports smooth compactly supported divergence-free initial data on R³ whose unforced three-dimensional incompressible Euler solution has finite maximal lifespan, with unbounded velocity gradient and divergent time integral of maximum vorticity.
Read original source Original Euler manuscript, Theorem 1.1cdn.openai.com
Original report: 2026-09-08For every positive viscosity, the manuscript reports a three-dimensional incompressible Navier–Stokes flow starting from rest with smooth compactly supported forcing, bounded kinetic energy, and unbounded velocity in finite time. It claims Clay alternatives C on R³ and D on the periodic torus.
Read original source Original manuscript, Theorem 1.1cdn.openai.com
Original report: 2026-09-08OpenAI claims globally smooth unique evolution for arbitrary admissible large initial data in the three-dimensional one-species relativistic Vlasov–Maxwell model, under its support and field assumptions.
Read original source Pinned primary manuscript · family 362github.com
Original report: 2026-10-06PDE research follows existence, uniqueness, regularity, and blowup for specified equations and initial data. Weak existence is different from global smooth uniqueness.
Background review: 2026-10-11. Selected sources:
Publication dates and editorial changes.
OpenAI reports: Global classical relativistic Vlasov–Maxwell solutions
Allow optional Google Analytics to help improve AIProofWatch? Privacy details.
