In this paper, we study the long-time existence of smooth solutions to the Cauchy problem for the Boussinesq equation with large initial data in $\mathbb{R}^n$. Due to the strong dispersive effect in the Boussinesq equation, the method of combining the blowup criterion and Strichartz estimate are used to show that the lifespan of the solutions can be taken arbitrarily large provided that the dispersive coefficient is large enough.

中文翻译：

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在 $\mathbb{R}^n$ 中具有大量初始数据的 Boussinesq 方程的长期存在性

在本文中，我们研究了在 $\mathbb{R}^n$ 中具有大量初始数据的 Boussinesq 方程柯西问题的光滑解的长期存在性。由于 Boussinesq 方程的色散效应很强，采用膨胀准则和 Strichartz 估计相结合的方法表明，只要色散系数足够大，解的寿命可以取任意大。