3 papers
math.AP2026
Weak Solutions for Inviscid SQG with Lorentz Data
Peter Constantin, Mihaela Ignatova, Quoc-Hung Nguyen
We construct global weak solutions of the inviscid surface quasi-geostrophic equation in and in smooth bounded domains, for arbitrary initial data in the critical Lor…
math.AP2026
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…
math.AP2025
Electroconvection in a Magnetic Field
Elie Abdo, Peter Constantin, Mihaela Ignatova +1
Electroconvection in a porous medium under a strong transversal magnetic field is described by an active scalar equation for the charge density. The equation has global weak soluti…