Well-posedness of the Stokes–Coriolis system in the half-space over a rough surface
Well-posedness of the Stokes–Coriolis system in the half-space over a rough surface
复制标题
粗糙表面半空间中斯托克斯-科里奥利系统的适定性
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Christophe Prange
中科院分区：
文献类型：
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作者：
Anne;Christophe Prange
本文研究了具有粗糙底的半空间中的定常3d Stokes-Coriolis方程组的适定性，其Dirichlet数据在空间无穷远处不减.我们的系统是Ekman边界层系统的线性化版本。我们在Sobolev正则空间中寻找无穷大能量的解。遵循Gerard-Varet和Masmoudi的想法，一般策略是将问题简化为在垂直方向上有界的颠簸通道，这要归功于涉及Dirichlet到Neumann算子的透明边界条件。我们的分析强调了在低切向频率的斯托克斯-科里奥利算子的一些强奇异性。本文工作的主要特点之一是定义了一个关于Kato空间H^{1/2}_{uloc}$中Stokes-Coriolis系统的Dirichlet到Neumann算子。
This paper is devoted to the well-posedness of the stationary $3$d Stokes-Coriolis system set in a half-space with rough bottom and Dirichlet data which does not decrease at space infinity. Our system is a linearized version of the Ekman boundary layer system. We look for a solution of infinite energy in a space of Sobolev regularity. Following an idea of Gerard-Varet and Masmoudi, the general strategy is to reduce the problem to a bumpy channel bounded in the vertical direction thanks a transparent boundary condition involving a Dirichlet to Neumann operator. Our analysis emphasizes some strong singularities of the Stokes-Coriolis operator at low tangential frequencies. One of the main features of our work lies in the definition of a Dirichlet to Neumann operator for the Stokes-Coriolis system with data in the Kato space $H^{1/2}_{uloc}$.
具有非局域初始数据的重力水波系统的柯西理论
DOI：
10.48550/arxiv.1305.0457
发表时间：
2013
期刊：
arXiv e-prints
影响因子：
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作者：
Alazard Thomas
通讯作者：
Alazard Thomas