Zobrazeno 1 - 10
of 36
pro vyhledávání: '"Ai, Albert"'
Autor:
Ai, Albert, Liu, Grace
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 $L^2$, by using a discretized gauge transform in the setting of Bourgain sp
Externí odkaz:
http://arxiv.org/abs/2407.01472
Autor:
Ai, Albert, Avadanei, Ovidiu-Neculai
We consider the well-posedness of the generalized surface quasi-geostrophic (gSQG) front equation. By using the null structure of the equation via a paradifferential normal form analysis, we obtain balanced energy estimates, which allow us to prove t
Externí odkaz:
http://arxiv.org/abs/2311.07551
Autor:
Ai, Albert, Avadanei, Ovidiu-Neculai
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 water waves system and nonlinear waves, have demonstrated that in pres
Externí odkaz:
http://arxiv.org/abs/2310.20143
Autor:
Ai, Albert
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 $H^s$, with $s > \frac{d}{2} + 2 - \mu$, with $\mu = \frac{3}{14}$ and $\mu = \frac37$
Externí odkaz:
http://arxiv.org/abs/2308.16176
Autor:
Ai, Albert, Avadanei, Ovidiu-Neculai
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 convergence condition on an expansion of the equation's nonlinearity. In t
Externí odkaz:
http://arxiv.org/abs/2212.00117
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 improved compared to the sharp results of Smith-Tataru for the generic
Externí odkaz:
http://arxiv.org/abs/2110.15296
Autor:
Ai, Albert, Avadanei, Ovidiu-Neculai
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, and although the equation has formal similarities with the KdV equat
Externí odkaz:
http://arxiv.org/abs/2105.01221
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 on global solutions for small and localized data. Such solutions have
Externí odkaz:
http://arxiv.org/abs/2009.11513
This article represents the first installment of a series of papers concerned with low regularity solutions for the water wave equations in two space dimensions. Our focus here is on sharp cubic energy estimates. Precisely, we introduce and develop t
Externí odkaz:
http://arxiv.org/abs/1910.05323
Autor:
Ai, Albert1 (AUTHOR), Ifrim, Mihaela1 (AUTHOR), Tataru, Daniel2 (AUTHOR) tataru@math.berkeley.edu
Publikováno v:
Inventiones Mathematicae. Mar2024, Vol. 235 Issue 3, p745-891. 147p.
