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摘要
In this paper, we will derive the two-dimensional extended Green-Naghdi system {see Matsuno [Proc. R. Soc. A 472, 20160127 (2016)] for determination in a various way} for flat bottoms of order three with respect to the shallowness parameter mu. Then we consider the 1D extended Green-Naghdi equations taking into account the effect of small surface tension. We show that the construction of solution with a standard Picard iterative scheme can be accomplished in which the well-posedness in X-s = Hs+2(R) x Hs+2(R) for some s > 3/2 of the new extended 1D system for a finite large time existence t = O(1/epsilon) is demonstrated. Published by AIP Publishing.
- 出版日期2018-7
