Decay of Weak Solutions to the 2D Dissipative Quasi-Geostrophic Equation |
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Authors: | César J Niche María E Schonbek |
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Institution: | (1) Department of Mathematics, UC Santa Cruz, Santa Cruz, CA 95064, USA |
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Abstract: | We address the decay of the norm of weak solutions to the 2D dissipative quasi-geostrophic equation. When the initial data
θ0 is in L
2 only, we prove that the L
2 norm tends to zero but with no uniform rate, that is, there are solutions with arbitrarily slow decay. For θ0 in L
p
∩ L
2, with 1 ≤ p < 2, we are able to obtain a uniform decay rate in L
2. We also prove that when the norm of θ0 is small enough, the L
q
norms, for , have uniform decay rates. This result allows us to prove decay for the L
q
norms, for , when θ0 is in .
The second author was partially supported by NSF grant DMS-0600692. |
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Keywords: | |
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