Energy Decay for a Weak Solution of the Navier–Stokes Equation with Slowly Varying External Forces
Energy Decay for a Weak Solution of the Navier–Stokes Equation with Slowly Varying External Forces
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DOI：
10.1006/jfan.1996.3011
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发表时间：
1997-03
影响因子：
1.7
通讯作者：
T. Ogawa;S. Rajopadhye;M. Schonbek
中科院分区：
文献类型：
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作者：
T. Ogawa;S. Rajopadhye;M. Schonbek
我们考虑具有缓慢衰减外力的纳维-斯托克斯系统[公式]我们证明，在数据f和a的适当条件下，弱解的能量范数具有非均匀衰减，‖u(t)‖2→0 (t→∞)，使得解的能量在时间上有界。此外，我们还显示了具有给定显式衰减率的外力的能量衰减（均匀衰减）的准确速率，‖u(t)‖2⩽C(1+t)−e。
We consider the Navier–Stokes system with slowly decaying external forces[formula]We show that the energy norm of a weak solution has non-uniform decay,‖u(t)‖2→0 (t→∞),under suitable conditions on the data f and a which make the energy of solution bounded in time. Also, we show the exact rate of the decay (uniform decay) of the energy,‖u(t)‖2⩽C(1+t)−e,for external forces with a given explicit decay rate.