17 citations · 28 across the 9 of their papers we have counts for
10 papers
Liouville Theorems for the Stationary Fractional Magnetohydrodynamic Equations
Albert Ai, Gaston Vergara-Hermosilla
We establish Liouville-type theorems for the three-dimensional stationary fractional magnetohydrodynamic (MHD) system with different orders of dissipation. Our first result shows t…
Improved low regularity theory for gravity-capillary waves
Albert Ai
This article concerns the Cauchy problem for the gravity-capillary water waves system in general dimensions. We establish local well-posedness for initial data in , with $s >…
Well-posedness for the surface quasi-geostrophic front equation
Albert Ai, Ovidiu-Neculai Avadanei
We consider the well-posedness of the surface quasi-geostrophic (SQG) front equation. Hunter-Shu-Zhang [9] established well-posedness under a small data condition as well as a conv…
The time-like minimal surface equation in Minkowski space: low regularity solutions
Albert Ai, Mihaela Ifrim, Daniel Tataru
It has long been conjectured that for nonlinear wave equations which satisfy a nonlinear form of the null condition, the low regularity well-posedness theory can be significantly i…
Well-posedness for the dispersive Hunter-Saxton equation
Albert Ai, Ovidiu-Neculai Avadanei
This article represents a first step towards understanding the well-posedness for the dispersive Hunter-Saxton equation. This problem arises in the study of nematic liquid crystals…
Two dimensional gravity waves at low regularity II: Global solutions
Albert Ai, Mihaela Ifrim, Daniel Tataru
This article represents the second installment of a series of papers concerned with low regularity solutions for the water wave equations in two space dimensions. Our focus here is…