Existence and Uniqueness of Time-Periodic Solutions to the Semigeostrophic Equations - Rahman, Mohammad; Wang, Kening; Zhan, Mei-Qin (Journal of Applied Nonlinear Dynamics, 2026)
In this article, we study the Semigeostrophic Equations in meteorology. These equations were introduced by Hoskins and Bretherton [1]. After suitable changes of variables, one can obtain the following coupled the Monge-Ampère/Transport problem aligned qt + J(ψ, q)=0 Δ φ + (^2 φx_i x_j)+ 1 = q onumber ψ_xx φ_yy - 2 ψ_xy φ_xy + ψ_yy φ_xx + Δ ψ -Δ φ = 0 aligned We proved the existence and uniqueness of time-periodic solution to the system.