摘要
In this paper,we study the one-dimensional motion of viscous gas near a vacuum,with the gas connecting to a vacuum state with a jump in density.The interface behavior,the pointwise decay rates of the density function and the expanding rates of the interface are obtained with the viscosity coefficientμ(ρ)=ρ^(α)for any 0<α<1;this includes the timeweighted boundedness from below and above.The smoothness of the solution is discussed.Moreover,we construct a class of self-similar classical solutions which exhibit some interesting properties,such as optimal estimates.The present paper extends the results in[Luo T,Xin Z P,Yang T.SIAM J Math Anal,2000,31(6):1175-1191]to the jump boundary conditions case with density-dependent viscosity.
作者
郭真华
张学耀
Zhenhua GUO;Xueyao ZHANG(School of Mathematics and CNS,Northwest University,Xi’an,710127,China;School of Mathematics and Information Science,Guangxi University,Nanning,530004,China)
基金
supported by the NSFC(11931013)
the GXNSF(2022GXNSFDA035078)。
