We study the ocean flow in Arctic gyres using a recent model for gyres derived in spherical coordinates on the rotating sphere. By projecting this model onto the plane using the Mercator projection, we obtain a semi-linear elliptic partial differential equation in an unbounded domain, difficulty which is then overcome by projecting the PDE onto the unit disk via a conformal map. We then study existence, regularity and uniqueness of solutions for constant and linear vorticity functions.

中文翻译：

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椭圆型偏微分方程的海洋偏流模拟研究

我们使用在旋转球体的球坐标中派生的回旋模型的最新模型研究了北极回旋中的海洋流动。通过使用Mercator投影将该模型投影到平面上，我们在无界域中获得了一个半线性椭圆型偏微分方程，然后通过通过保形图将PDE投影到单位圆盘上克服了这一难题。然后，我们研究常数和线性涡旋函数解的存在性，正则性和唯一性。