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arXiv · 2108.13117

Wellposedness and scattering for the generalized Boussinesq equation

Jie Chen·Boling Guo·Jie Shao
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Abstract

In this paper, we show the local well-posedness of the generalized Boussinesq equation(gBQ) in $L^{2}(\mathbb{R}^d), H^{1}(\mathbb{R}^d)$ and obtain the global well-posedness, finite-time blowup and small initial data scattering of gBQ in energy space $H^1(\mathbb{R}^d)$. Moreover, we obtain the large radial initial data scattering of defocusing case for $ d\geq 3 $ by using the method of Dodson-Murphy.

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Jie Chen, Boling Guo, Jie Shao. 2021-08-30. Wellposedness and scattering for the generalized Boussinesq equation. https://arxiv.org/abs/2108.13117

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