在本論文中，在分析Shallow water equation 時，通常會先探討伴隨科氏力的三維Navier-Stokes Equation，接著會忽略垂直數度分布，將三維的Navier-Stokes Equation 推導成二維的Shallow water equation，並同乘以一個旋轉矩陣，使二維的Shallow water equation 消去source term。可在對稱空間中做座標轉換，進而使二維的Shallow water equation 成為一雙曲型系統的conservation laws。 In this paper , we consider the following three dimension shallow water equations with Coriolis force then we derived the two dimension shallow water equation . And we transformed the two dimension shallow water equation 3by3 conservative system without source term . We can use the results in traditional hyperbolic systems of conservation laws to study the shock waves and rarefaction waves.
