4 papers
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…
Low regularity solutions for gravity water waves II: The 2D case
Albert Ai
The gravity water waves equations describe the evolution of the surface of an incompressible, irrotational fluid in the presence of gravity. The classical regularity threshold for…
Sylvester-Gallai type theorems for approximate collinearity
Albert Ai, Zeev Dvir, Shubhangi Saraf +1
We study questions in incidence geometry where the precise position of points is `blurry' (e.g. due to noise, inaccuracy or error). Thus lines are replaced by narrow tubes, and mor…