Weak solutions for generalized large-scale semigeostrophic equations
Weak solutions for generalized large-scale semigeostrophic equations
复制标题
广义大规模半地转方程的弱解
DOI：
10.3934/cpaa.2013.12.939
复制
发表时间：
2012
影响因子：
1
通讯作者：
M. Oliver
中科院分区：
文献类型：
--
作者：
Mahmut Çalık;M. Oliver
我们证明了存在性、唯一性和对初始
广义大尺度方程整体弱解的数据
具有周期边界条件的半地转方程这
快速旋转浅流体的Hamilton平衡模型族
水包括由R. 1985年，
2006年，第二作者。分析是基于
涡量公式的模式补充了一个非线性
速度-涡度关系结果从根本上说是由于
位涡守恒虽然经典的解决方案是
如果初始位涡是
积极的-一个已经隐含在形式中的条件
平衡模型的推导，我们可以断言弱
只有在稍微强一点的假设下，
位涡的边界为$\sqrt{5}-2$乘以
平衡位涡原因是
位涡反演的非线性更明显
在较弱的函数空间中工作。另一
这种效应的表现是，点涡解不是
即使在特殊情况下，
涡度反演在经典的
功能协调发展的
We prove existence, uniqueness and continuous dependence on initial
data of global weak solutions to the generalized large-scale
semigeostrophic equations with periodic boundary conditions. This
family of Hamiltonian balance models for rapidly rotating shallow
water includes the $L_1$ model derived by R. Salmon in 1985 and its
2006 generalization by the second author. The analysis is based on the
vorticity formulation of the models supplemented by a nonlinear
velocity-vorticity relation. The results are fundamentally due to the
conservation of potential vorticity. While classical solutions are
known to exist provided the initial potential vorticity is
positive---a condition which is already implicit in the formal
derivation of balance models, we can assert the existence of weak
solutions only under the slightly stronger assumption that the
potential vorticity is bounded below by $\sqrt{5}-2$ times the
equilibrium potential vorticity. The reason is that the
nonlinearities in the potential vorticity inversion are felt more
strongly when working in weaker function spaces. Another
manifestation of this effect is that point-vortex solutions are not
supported by the model even in the special case when the potential
vorticity inversion gains three derivatives in spaces of classical
functions.
影响因子：
2.5
作者：
M. Çalık;M. Oliver;S. Vasylkevych
通讯作者：
S. Vasylkevych