论文标题
局部存在用于弯曲结构域的半神经方程的平滑溶液
Local existence of smooth solutions for the semigeostrophic equations on curved domains
论文作者
论文摘要
我们证明了在平滑，有限和简单连接的$ \ mathbb {r}^2 $的平滑，有限和简单连接的域的一般环境中，可以在本地存在平滑的解决方案。我们介绍了在欧拉坐标中进行的建筑，避免了双重变量的经典重新进行，该重新构造在平坦的情况下使用恒定的科里奥利力，但在这个一般框架中缺乏。
We prove local-in-time existence of smooth solutions to the semigeostrophic equations in the general setting of smooth, bounded and simply connected domains of $\mathbb{R}^2$ endowed with an arbitrary conformally flat metric and non-vanishing Coriolis term. We present a construction taking place in Eulerian coordinates, avoiding the classical reformulation in dual variables, used in the flat case with constant Coriolis force, but lacking in this general framework.
