圆上广义Benjamin–Ono方程的低正则适定性

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Journal of Hyperbolic Differential Equations Pub Date : 2020-07-30 DOI:10.1142/S0219891621500272

Kihyun Kim, R. Schippa

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引用次数: 5

摘要

给出了具有四次或更高非线性和周期边界条件的广义Benjamin–Ono方程的新的低正则适定性结果。我们使用短时傅立叶变换限制方法和修正能量来克服导数损失。以前，Molinet–Ribaud通过规范变换在[公式：见正文]中建立了局部适定性。在不使用规范变换的情况下，我们在[公式：见文本]、[公式：看文本]中展示了局部存在性和先验估计，在[公式，见文本]中展现了局部适定性。在四次非线性的情况下，我们证明了以小初始数据为条件的解的全局存在性。

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Low regularity well-posedness for generalized Benjamin–Ono equations on the circle

New low regularity well-posedness results for the generalized Benjamin–Ono equations with quartic or higher nonlinearity and periodic boundary conditions are shown. We use the short-time Fourier transform restriction method and modified energies to overcome the derivative loss. Previously, Molinet–Ribaud established local well-posedness in [Formula: see text] via gauge transforms. We show local existence and a priori estimates in [Formula: see text], [Formula: see text], and local well-posedness in [Formula: see text], [Formula: see text] without using gauge transforms. In case of quartic nonlinearity we prove global existence of solutions conditional upon small initial data.

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来源期刊

Journal of Hyperbolic Differential Equations 数学-物理：数学物理

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： This journal publishes original research papers on nonlinear hyperbolic problems and related topics, of mathematical and/or physical interest. Specifically, it invites papers on the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising in mathematical physics. The Journal welcomes contributions in: Theory of nonlinear hyperbolic systems of conservation laws, addressing the issues of well-posedness and qualitative behavior of solutions, in one or several space dimensions. Hyperbolic differential equations of mathematical physics, such as the Einstein equations of general relativity, Dirac equations, Maxwell equations, relativistic fluid models, etc. Lorentzian geometry, particularly global geometric and causal theoretic aspects of spacetimes satisfying the Einstein equations. Nonlinear hyperbolic systems arising in continuum physics such as: hyperbolic models of fluid dynamics, mixed models of transonic flows, etc. General problems that are dominated (but not exclusively driven) by finite speed phenomena, such as dissipative and dispersive perturbations of hyperbolic systems, and models from statistical mechanics and other probabilistic models relevant to the derivation of fluid dynamical equations. Convergence analysis of numerical methods for hyperbolic equations: finite difference schemes, finite volumes schemes, etc.