AI 中文总结
本文针对任意空间维度下带二次与三次非线性项的六阶Boussinesq方程初值问题，通过Fourier限制范数方法与高低频分解建立其非线性光滑性，进而得到积分项的一致收敛性与空间衰减性。
AI 中文摘要
本文研究任意空间维度下带二次与三次非线性项的六阶Boussinesq方程的初值问题。首先，通过Fourier限制范数方法与高低频分解，建立该方程的非线性光滑性，即Duhamel公式解的积分形式比其线性对应项具有更高正则性。最后，利用该非线性光滑性，对每个固定的t，建立积分项的一致收敛性及其空间衰减性。
英文摘要
In this paper, we study the initial value problem of the sixth-order Boussinesq equation with quadratic and cubic nonlinearities in arbitrary spatial dimensions. First, by using the Fourier restriction norm method and a high-low frequency decomposition, we establish the nonlinear smoothing for this equation, namely, the integral form of the solution to the Duhamel formulation enjoys higher regularity than its linear counterpart. Finally, by using the nonlinear smoothing, we establish the uniform convergence of the integral term and its spatial decay for each fixed $t$.
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