论文标题
潮湿的水波玩具模型
A Toy Model for Damped Water Waves
论文作者
论文摘要
我们考虑了一个域中潮湿的水波系统的玩具模型$ω_t\ subset \ mathbb {t} \ times \ times \ mathbb {r} $。玩具模型基于Alazard-Burq-Zuily工作中得出的范例分化水波方程。我们利用的阻尼形式是Clamond等人为三维水波系统提出的改良海绵层。 al。我们表明，对于小库奇（Cauchy）数据，玩具模型的解决方案具有二次寿命。这是通过证明能量估计来完成的，其能量是由适当选择的向量场构建的。
We consider a toy model for a damped water waves system in a domain $Ω_t \subset \mathbb{T} \times \mathbb{R}$. The toy model is based on the paradifferential water waves equation derived in the work of Alazard-Burq-Zuily. The form of damping we utilize we utilize is a modified sponge layer proposed for the three-dimensional water waves system by Clamond, et. al. We show that, in the case of small Cauchy data, solutions to the toy model exhibit a quadratic lifespan. This is done via proving energy estimates with the energy being constructed from appropriately chosen vector fields.
