修正的Navier－Stokes方程的定常解

Stationary Solutions of the Modified Navier-Stokes Equations

考虑于１９６８年作为粘性不可压缩流的一个数学模型提出的修正的Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程的定常解的存在性，唯一性和吸引性．定常的修正的Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程是满足一定的单调性条件的拟线性椭圆方程组．利用逼近建立了一个一般的存在性定理，进而看到，如果或者椭圆性常数足够大，或者具适当大的单调性参数，或者外力相当小，则有唯一的定常解，最后，我们在类似（仅仅是类似！）于上述的条件下证明了所有的定常解的集合是极小的紧的不变的可吸引相空间中任何有界集的吸引子．

he existence,uniqueness and attractiveness of stationary solutions for the modified Navier-Stokes equations proposed by Ladyzhenskaya in 1968 as a mathematical model of the viscous in-compressible flows are considered.The stationary modified Navier-Stokes equations are a quasi-linear elliptic system satisfying a certain monotonicity condition.A general theorem of existence isestablished by the Galerkin approximation. Futhermore,it is shown that there is an unique sta-tionary solution if either the ellipticity constant is large enough,or the monotonicity parameter issuitably great, or the external force is appropriately small.Finally, under some conditions, it isproved that the set of all stationary solutions is the minimal compact invariant attractor which canattract any bounded set of the phase space.