Global strong Lp well-posedness of the 3D primitive equations with heat and salinity diffusion
Global strong Lp well-posedness of the 3D primitive equations with heat and salinity diffusion
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DOI：
10.1016/j.jde.2016.09.010
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发表时间：
2016-05
影响因子：
2.4
通讯作者：
Matthias Hieber;Amru Hussein;Takahito Kashiwabara
中科院分区：
文献类型：
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作者：
Matthias Hieber;Amru Hussein;Takahito Kashiwabara
考虑完整的原始方程，即三维原始方程耦合到温度和盐度方程，并受到外力的影响。证明了对于位于一定插值空间中的任意大初值，该方程组是全局强适定的，该插值空间被明确地刻画为H2/p，p，1< p<∞的子空间，满足一定的边界条件.特别地，对于可微性小于H1的初始数据，获得了完整原始方程的全局适定性，从而将Cao和Titi（2007）[5]的结果推广到非光滑数据的情况。此外，它表明，解决方案是指数衰减提供的外力具有这种性质。
Consider the full primitive equations, ie the three dimensional primitive equations coupled to the equation for temperature and salinity, and subject to outer forces. It is shown that this set of equations is globally strongly well-posed for arbitrary large initial data lying in certain interpolation spaces, which are explicitly characterized as subspaces of H 2/p, p, 1< p<∞, satisfying certain boundary conditions. In particular, global well-posedness of the full primitive equations is obtained for initial data having less differentiability properties than H 1, hereby generalizing a result by Cao and Titi (2007)[5] to the case of non-smooth data. In addition, it is shown that the solutions are exponentially decaying provided the outer forces possess this property.