论文标题
关键案例的Korteweg类型可压缩流体模型的全球适合性
The global well-posedness of the compressible fluid model of Korteweg type for the critical case
论文作者
论文摘要
在本文中，我们将Korteweg类型的可压缩流体模型考虑在一个关键情况下，在给定恒定状态下，压力的导数等于$ 0 $。结果表明，该系统在Maximal $ L_P $ -L_Q $常规类中采用了独特的，全球强的解决方案，用于小型初始数据。结果，我们还证明了非线器问题解决方案的衰减估计值。为了获得关键案例的全局良好性，我们显示了$ l_p $ - $ l_q $ decay属性在低频的额外假设下向线性化方程式的解决方案的衰减属性。
In this paper, we consider the compressible fluid model of Korteweg type in a critical case where the derivative of pressure equals to $0$ at the given constant state. It is shown that the system admits a unique, global strong solution for small initial data in the maximal $L_p$-$L_q$ regularity class. As a result, we also prove the decay estimates of the solutions to the nonliner problem. In order to obtain the global well-posedness for the critical case, we show $L_p$-$L_q$ decay properties of solutions to the linearized equations under an additional assumption for a low frequencies.
