On the Cauchy problem for a generalized two-component shallow water wave system with fractional higher-order inertia operators
On the Cauchy problem for a generalized two-component shallow water wave system with fractional higher-order inertia operators
In this paper, we mainly consider the Cauchy problem for a generalized two-component shallow water wave system with fractional higher-order inertia operators: $m=(1-\partial_x^2)^su, s>1$. By Littlewood-Paley theory and transport equation theory, we first establish the local well-posedness of the generalized b-equation with fractional higher-order inertia operators which is the subsystem …