In this paper, we consider the initial-boundary problem for a 1D two-fluid model with densitydependent viscosity and vacuum. The pressure depends on two variables but the viscosity only depends on one of the densities...In this paper, we consider the initial-boundary problem for a 1D two-fluid model with densitydependent viscosity and vacuum. The pressure depends on two variables but the viscosity only depends on one of the densities. We prove the global existence and uniqueness of the classical solution in the one-dimensional space with large initial data and vacuum. We use a new Helmholtz free energy function and the material derivative of the velocity field to deal with the general pressure with two variables, without the equivalence condition. We also develop a new argument to handle the general viscosity.展开更多
基金supported by the Shantou University funding(Grant No.NTF20025)National Natural Science Foundation of China(Grant No.12101386)+1 种基金supported by National Natural Science Foundation of China(Grant Nos.12171160,11771150 and 11831003)Guangdong Basic and Applied Basic Research Foundation(Grant No.2020B1515310015)。
文摘In this paper, we consider the initial-boundary problem for a 1D two-fluid model with densitydependent viscosity and vacuum. The pressure depends on two variables but the viscosity only depends on one of the densities. We prove the global existence and uniqueness of the classical solution in the one-dimensional space with large initial data and vacuum. We use a new Helmholtz free energy function and the material derivative of the velocity field to deal with the general pressure with two variables, without the equivalence condition. We also develop a new argument to handle the general viscosity.
