Continuity Properties and Global Attractors of Generalized Semiflows and the Navier-Stokes Equations
Continuity Properties and Global Attractors of Generalized Semiflows and the Navier-Stokes Equations
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DOI：
10.1007/s003329900037
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发表时间：
1997
影响因子：
3
通讯作者：
J. Ball
中科院分区：
文献类型：
--
作者：
J. Ball
定义了一类可能具有非唯一解的半流。研究了这类广义半流的可测性和连续性。证明了广义半流有全局吸引子当且仅当它是逐点耗散的且渐近紧的。研究了在李雅普诺夫函数存在下的全局吸引子的结构、连通性和稳定性。特别地，给出了整体吸引子是单点但不稳定的例子，在所有弱解从（0，∞）到L2连续的假设下，证明了三维不可压Navier-Stokes方程整体吸引子的存在性.
A class of semiflows having possibly nonunique solutions is defined. The measurability and continuity properties of such generalized semiflows are studied. It is shown that a generalized semiflow has a global attractor if and only if it is pointwise dissipative and asymptotically compact. The structure of the global attractor in the presence of a Lyapunov function, and its connectedness and stability properties are studied. In particular, examples are given in which the global attractor is a single point but is not Lyapunov stable.The existence of a global attractor for the 3D incompressible Navier-Stokes equations is established under the (unproved) hypothesis that all weak solutions are continuous from (0, ∞) toL2.