Convergence rate of hypersonic similarity for steady potential flows over two-dimensional Lipschitz wedge

This paper is devoted to establishing the convergence rate of hypersonic similarity for inviscid steady irrotational Euler flow over a two-dimensional Lipschitz slender wedge in $$BV\cap L^1$$ space. The we established same as one predicted by Newtonian-Busemann law (see (3.29) [2, p 67] more details) incoming Mach number $$\text {M}_{\infty }\rightarrow \infty $$ fixed parameter K. similarity, which also called Mach-number independence principle, equivalent following Van Dyke’s theory: For given K, when sufficiently large, governing equations after scaling are approximated simpler equation, that small-disturbance equation. To achieve rate, approximate curved boundary piecewisely straight lines and find new continuous map $$\mathcal {P}_{h}$$ such trajectory can be obtained piecing together Riemann solutions near boundary. Next, derive $$L^1$$ difference estimates between $$U^{(\tau )}_{h,\nu }(x,\cdot )$$ initial-boundary value problem scaled trajectories {P}_{h}(x,0)(U^{\nu }_{0})$$ all solvers. Then, uniqueness compactness }$$ , further establish order $$\tau ^2$$ equations, if total variations initial data tangential derivative small. Based on it, better considering past wing show length with effect scale $$O(\tau ^{-1})$$ is, two ^{\frac{3}{2}})$$ under assumption perturbation has compact support.