Výsledky vyhledávání - "Sanwal, Akansha"

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Improved well-posedness for quasilinear and sharp local well-posedness for semilinear KP-I equations

Autor: Kinoshita, Shinya, Sanwal, Akansha, Schippa, Robert

We show new well-posedness results in anisotropic Sobolev spaces for dispersion-generalized KP-I equations with increased dispersion compared to the KP-I equation. We obtain the sharp dispersion rate, below which generalized KP-I equations on $\mathb

Externí odkaz: http://arxiv.org/abs/2408.16348

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Low regularity well-posedness of KP-I equations: the three-dimensional case

Autor: Herr, Sebastian, Sanwal, Akansha, Schippa, Robert

Publikováno v: J. Funct. Anal. (2024), vol. 286, no. 4, article 110292

In this paper, low regularity local well-posedness results for the Kadomtsev--Petviashvili--I equation posed in spatial dimension $d =3$ are proved. Periodic, non-periodic and mixed settings as well as generalized dispersion relations are considered.

Externí odkaz: http://arxiv.org/abs/2212.14067

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Decoupling inequality for paraboloid under shell type restriction and its application to the periodic Zakharov system

Autor: Kinoshita, Shinya, Nakamura, Shohei, Sanwal, Akansha

In this paper, we establish local well-posedness for the Zakharov system on $\mathbb{T}^d$, $d\ge3$ in a low regularity setting. Our result improves the work of Kishimoto. Moreover, the result is sharp up to $\varepsilon$-loss of regularity when $d=3

Externí odkaz: http://arxiv.org/abs/2212.01805

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Low regularity well-posedness for KP-I equations: the dispersion-generalized case

Autor: Sanwal, Akansha, Schippa, Robert

We prove new well-posedness results for dispersion-generalized Kadomtsev--Petviashvili I equations in $\mathbb{R}^2$, which family links the classical KP-I equation with the fifth order KP-I equation. For strong enough dispersion, we show global well

Externí odkaz: http://arxiv.org/abs/2205.02037

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Local Well-Posedness for the Zakharov System in Dimension $d\leqslant 3$

Autor: Sanwal, Akansha

Publikováno v: Discrete and Continuous Dynamical Systems, 2022, 42 (3) : 1067-1103

The Zakharov system in dimension $d\leqslant 3$ is shown to be locally well-posed in Sobolev spaces $H^s \times H^l$, extending the previously known result. We construct new solution spaces by modifying the $X^{s,b}$ spaces, specifically by introduci

Externí odkaz: http://arxiv.org/abs/2103.09259

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