Resolvent Estimates for a Compressible Fluid Model of Korteweg Type and Their Application
Resolvent Estimates for a Compressible Fluid Model of Korteweg Type and Their Application
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DOI：
10.1007/s00021-021-00646-3
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发表时间：
2021-12
影响因子：
1.3
通讯作者：
Takayuki Kobayashi;M. Murata;Hirokazu Saito
中科院分区：
文献类型：
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作者：
Takayuki Kobayashi;M. Murata;Hirokazu Saito
在本文中，我们考虑了由Dunn和Serrin（1985）导出的等温可压缩粘性流体的Korteweg型模型的一个预解问题，并证明了在有界区域和外部区域中的预解估计。采用Korteweg型模型描述流体毛细效应或具有相变的液-汽两相流作为扩散界面模型。我们的预解问题是从一个线性系统的Korteweg型模型的稳定状态，其中是流体密度和流体速度。对于有界区域，我们处理了变系数问题，证明了在压力函数不仅满足而且满足的条件下，预解集包含。我们遵循Kotschote（2014）的思想来处理。对于外区域，我们处理常系数，并证明了预解集包含对任何时候。此外，作为预解式估计的应用，我们引入了有界区域上非线性问题的全局可解性结果。
In this paper, we consider a resolvent problem arising in the study of a Korteweg-type model of isothermal compressible viscous fluids derived by Dunn and Serrin (1985), and we prove resolvent estimates in bounded and exterior domains. The Korteweg-type model is employed to describe fluid capillarity effects or a liquid-vapor two-phase flow with phase transition as diffuse interface model. Our resolvent problem is obtained from a linearized system of the Korteweg-type model around the steady state, whereis the fluid density andis the fluid velocity. For bounded domains, we treat variable coefficients and prove that the resolvent set containsunder the condition that the pressure functionsatisfies not onlybut also, where. We follow the idea of Kotschote (2014) to handle. For exterior domains, we treat constant coefficients and prove that the resolvent set containsfor anywhen. Furthermore, we introduce a global solvability result for the nonlinear problem in a bounded domain as an application of the resolvent estimate.