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math.AP2024★ 1 cited
The dispersion generalized Benjamin-Ono equation
Albert Ai, Grace Liu
We consider the well-posedness of the family of dispersion generalized Benjamin-Ono equations. Earlier work of Herr-Ionescu-Kenig-Koch established well-posedness with data in …
math.AP2023★ 2 cited
Low regularity solutions for the surface quasi-geostrophic front equation
Albert Ai, Ovidiu-Neculai Avadanei
In this article we consider the low regularity well-posedness of the surface quasi-geostrophic (SQG) front equation. Recent work on other quasilinear models, including the gravity…
math.AP2023★ 1 cited
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 >…