标题： 准地转模型中非周期粗糙海岸附近的边界层形成 显示英文标题

标题： Boundary layer formation in the quasigeostrophic model near nonperiodic rough coasts

摘要： 我们研究所谓的风驱动海洋环流的均匀模型，也称为单层准地转模型。 我们的注意力集中在进行完整的渐近分析，突出沿海岸线的边界层形成。 我们假设粗糙的海岸没有任何特殊结构，导致在无限域中研究西部边界层的非线性偏微分方程组。 因此，我们在非局部Sobolev空间中寻找解。 在这一假设下，东部边界层在远离粗糙边界处的低频下表现出奇异行为，导致收敛问题。 通过施加遍历性性质来解决这个问题。 我们建立了控制边界层方程和近似解的适定性。 我们的结果在周期性不规则性的背景下推广了Bresch和Gérard-Varet（Commun. Math. Phys. (1) 253: (2005), 81-119）论文中的结果。 显示英文摘要

摘要： We study the so-called homogeneous model of wind-driven ocean circulation, also known as the single-layer quasigeostrophic model. Our attention focuses on performing a complete asymptotic analysis that highlights boundary layer formation along the coastal line. We assume rough coasts without any particular structure, resulting in the study of a nonlinear PDE system for the western boundary layer in an infinite domain. As a consequence, we look for the solution in nonlocalized Sobolev spaces. Under this hypothesis, the eastern boundary layer exhibits a singular behavior at low frequencies far from the rough boundary leading to issues with convergence. The problem is tackled by imposing ergodicity properties. We establish the well-posedness of the governing boundary layer equations and the approximate solution. Our results generalize the ones in the paper of Bresch and G\'erard-Varet (Commun. Math. Phys. (1) 253: (2005), 81-119) in the context of periodic irregularities.