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Nonuniform dependence of the R-b-family system in Besov spaces
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2021-02-26 , DOI: 10.1002/zamm.202000329
John Holmes 1 , Ryan C. Thompson 2 , Feride Tiğlay 3
Affiliation  

In this paper, we consider a generalized rotation b-family system (R-b-family system) which models the evolution of equatorial water waves. Based on local well-posedness results and lifespan estimates, we establish sharpness of continuity on the data-to-solution map by showing that it is not uniformly continuous from B p , r s × B p , r s 1 to C ( [ 0 , T ] ; B p , r s × B p , r s 1 ) . The proof of nonuniform dependence is based upon approximate solutions and Littlewood-Paley decomposition theory.

中文翻译:

Besov 空间中 Rb 族系统的非均匀依赖

在本文中,我们考虑了一个广义旋转 b 族系统(Rb 族系统),它模拟了赤道水波的演化。基于局部适定性结果和寿命估计,我们在数据到解图上建立了连续性的锐度,方法是显示它不是均匀连续的 , r × , r - 1 ( [ 0 , ] ; , r × , r - 1 ) . 非均匀依赖的证明基于近似解和 Littlewood-Paley 分解理论。
更新日期:2021-02-26
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