Pointwise convergence problem of the one-dimensional Boussinesq-type equation

被引：0

作者：

Wang, Weimin ^{[1
]}

Yan, Wei ^{[1
]}

Zhang, Yating ^{[1
]}

机构：

[1] Henan Normal Univ, Sch Math & Informat Sci, Xinxiang 453007, Henan, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2024年

关键词：

Boussinesq equation; pointwise convergence problem; Strichartz estimates; LOCAL WELL-POSEDNESS; MAXIMAL-FUNCTION; SCHRODINGER-EQUATIONS; GLOBAL EXISTENCE; SOBOLEV SPACES; SCATTERING; REGULARITY; STABILITY;

D O I：

10.1002/mma.10408

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the initial data problem of the one-dimensional Boussinesq-type equation. Inspired by the work of Compaan et al. (Int. Math. Res. Not. 2021, 599-650), by using the Fourier restriction norm method, we investigate the pointwise convergence of the one-dimensional Boussinesq equation and cubic Boussinesq equation. We also only use the Strichartz estimates instead of Fourier restriction norm method to establish convergence conclusions of the one-dimensional cubic Boussinesq equation. The key ingredients are some Strichartz estimates and high-low frequency decomposition related to the nonlinear part of the integral form solution in the Duhamel form and the maximal function estimate related to inhomogeneous estimate.

引用

页码：1750 / 1767

页数：18

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