Decay of Weak Solutions to the 2D Dissipative Quasi-Geostrophic Equation
Decay of Weak Solutions to the 2D Dissipative Quasi-Geostrophic Equation
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DOI：
10.1007/s00220-007-0327-y
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发表时间：
2006-05
影响因子：
2.4
通讯作者：
C. J. Niche;M. Schonbek
中科院分区：
文献类型：
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作者：
C. J. Niche;M. Schonbek
研究了二维耗散准地转方程弱解范数的衰减。当初始值θ 0仅在L2中时，我们证明了L2范数趋于零，但没有一致速率，即存在任意慢衰减的解.对于Lp中的θ 0 <$L2，当1 ≤p< 2时，我们能够得到L2中的均匀衰减率。我们还证明了当θ 0的m足够小时，对于的Lq范数具有一致衰减率。这个结果使我们能够证明当θ 0在时，对于，Lq范数是衰减的。
We address the decay of the norm of weak solutions to the 2D dissipative quasi-geostrophic equation. When the initial data θ0is inL2only, we prove that theL2norm tends to zero but with no uniform rate, that is, there are solutions with arbitrarily slow decay. For θ0inLp∩L2, with 1 ≤p< 2, we are able to obtain a uniform decay rate inL2. We also prove that when thenorm of θ0is small enough, theLqnorms, for, have uniform decay rates. This result allows us to prove decay for theLqnorms, for, when θ0is in.