A Fully Nonlinear Version of the Incompressible Euler Equations: The Semigeostrophic System
A Fully Nonlinear Version of the Incompressible Euler Equations: The Semigeostrophic System
复制标题
不可压缩欧拉方程的完全非线性版本：半地转系统
DOI：
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发表时间：
2006
影响因子：
2
通讯作者：
G. Loeper
中科院分区：
文献类型：
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作者：
G. Loeper
半地转方程用于气象学。它们表现为涡量形式的二维欧拉不可压方程的一种变体，其中将流函数和涡量场联系起来的泊松方程只是被完全非线性椭圆型Monge-Ampere方程所取代。这项工作收集了关于半地转方程的新结果：测度值解的存在性和稳定性，在密度的某些连续条件下解的存在性和唯一性，以及收敛到不可压缩欧拉方程。
The semigeostrophic equations are used in meteorology. They appear as a variant of the two‐dimensional Euler incompressible equations in vorticity form, where the Poisson equation that relates the stream function and the vorticity field is just replaced by the fully nonlinear elliptic Monge–Ampere equation. This work gathers new results concerning the semigeostrophic equations: existence and stability of measure‐valued solutions, existence and uniqueness of solutions under certain continuity conditions for the density, and convergence to the incompressible Euler equations.