Abstract

We prove a long time existence result for the solutions of a two-dimensional Boussinesq system modeling the propagation of long, weakly nonlinear water waves. This system is exceptional in the sense that it is the only linearly well-posed system in the (abcd) family of Boussinesq systems whose eigenvalues of the linearized system have nontrivial zeroes. This new difficulty is solved by the use of “good unknowns” and of normal form techniques.

中文翻译：

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二维强色散Boussinesq系统的长期存在性

摘要

我们证明了一个二维 Boussinesq 系统的解的长期存在结果，该系统对长的、弱非线性水波的传播进行建模。该系统是例外的，因为它是 Boussinesq 系统 (abcd) 族中唯一的线性适定系统，其线性化系统的特征值具有非平凡零点。这个新的困难是通过使用“好的未知数”和范式技术来解决的。