摘要
This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/4.Furthermore,we obtain the global C^(∞)-solutions if the initial data is smooth.
作者
丁时进
李颖花
王喻
Shijin DING;Yinghua LI;Yu WANG(School of Mathematical Sciences,South China Normal University,Guangzhou,510631,China)
基金
supported by the Key Project of the NSFC(12131010)
the NSFC(11771155,12271032)
the NSF of Guangdong Province(2021A1515010249,2021A1515010303)
supported by the NSFC(11971179,12371205)。
