一类含线性阻尼的非线性自治g-Navier-Stokes系统解的渐近光滑效应

The asymptotic smooth effect of solution for a nonlinear autonomous system with linear dampness

研究一类含线性阻尼的非线性自治g-Navier-Stokes系统解的渐近性,该文应用Young's不等式、Gronwall引理、全局吸引子存在性理论,证明了在Hg空间中的全局吸引子与Vg空间中的全局吸引子相等,得出含线性阻尼的非线性自治g-Navier-Stokes系统的解具有渐近光滑效应这一结论。

In this paper, the asymptotic properties of solution for a nonlinear autonomous g-Navier-Stokes sys- tem with linear dampness were investigated, with Young＇s inequality, Gronwall lemma and the existence theo- ry of global attractor. It was proved that the global attractors in Hg was equal to the global attractor in Vg. It was given the asymptotic smooth effect of solution for a nonlinear autonomous g-Navier-Stokessystem with linear dampness.