摘要
Under the assumptions that the initial density ρ0 is close enough to 1 and ρ0-1∈Hs+1(R2);u0∈Hs(R2)∩H_∈(R2) for s>2 and 0<ε<1;the authors prove the global existence and uniqueness of smooth solutions to the 2-D inhomogeneous Navier-Stokes equations with the viscous coefficient depending on the density of the fluid.Furthermore,the L2 decay rate of the velocity field is obtained.
Under the assumptions that the initial density ρ0 is close enough to 1 and ρ0 -- 1∈ H^s＋1（R^2）, u0 ∈ H^s（R^2） ∩ H^-ε（R^2） for s 〉 2 and 0 〈 ε 〈 1, the authors prove the global existence and uniqueness of smooth solutions to the 2-D inhomogeneous Navier-Stokes equations with the viscous coefficient depending on the density of the fluid. Furthermore, the L^2 decay rate of the velocity field is obtained.
基金
Project supported by the National Natural Science Foundation of China (Nos.10525101,10421101)
the 973 project of the Ministry of Science and Technology of China
the innovation grant from Chinese Academy of Sciences
