On the Effect of Rotation on the Life-Span of Analytic Solutions to the 3D Inviscid Primitive Equations

We study the effect of rotation on life-span solutions to 3D hydrostatic Euler equations with and inviscid Primitive (PEs) torus. The space analytic functions appears be natural initial value problem for PEs general data, as they have been recently shown exhibit Kelvin–Helmholtz type instability. First, a short interval time that is independent rate $$|\Omega |$$ , we establish local well-posedness in functions. In addition, thanks fine analysis barotropic baroclinic modes decomposition, two results about long existence solutions. (i) Independently show solution tends infinity norm mode goes zero. Moreover, this case converges limit system, which governed by 2D equations. (ii) can prolonged unboundedly |\rightarrow \infty $$ main result paper. This established “well-prepared” namely, when only Sobolev (but not norm) small enough, depending . Furthermore, large approximated simple resonant system same data.