Abstract:The potential systems and nonlocal conservation laws of Prandtl boundary layer equations on the surface of a sphere have been investigated. The multiplier approach yields two local conservation laws for the Prandtl boundary layer equations on the surface of a sphere. Two potential variables ψ and ϕ are introduced corresponding to first and second conservation law. Moreover, another potential variable p is introduced by considering the linear combination of both conservation laws. Two level one potential systems involving a single nonlocal variable ψ or ϕ are constructed. One level two potential system involving both nonlocal variables ψ and ϕ is established. The nonlocal variable p is utilised to derive a spectral potential system. The nonlocal conservation laws of Prandtl boundary layer equations on the surface of a sphere are derived by computing the local conservation laws of its potential systems. The nonlocal conservation laws are utilised to derive the further nonlocally related systems.
GPU‐accelerated simulation of a non‐local conservation law
