Convergence rate of the hypersonic similarity for two-dimensional steady potential flows with large data

Journal article

We establish the optimal convergence rate of the hypersonic similarity for two-dimensional steady potential flows with large data past a straight wedge in the $BV \cap L^1$ framework, provided that the total variation of the large data multiplied by $\gamma - 1 + \frac{a_\infty^2}{M_\infty^2}$ is uniformly bounded with respect to the adiabatic exponent $\gamma > 1$, the Mach number $M_\infty$ of the incoming steady flow, and the hypersonic similarity parameter $a_\infty$. Our main approach in this paper is first to establish the well-posedness and the Lipschitz continuous map $\mathcal{P}$ that has the properties similar to the Standard Riemann Semigroup of the initial-boundary value problem for the isothermal hypersonic small disturbance equations with large data, and then to compare the Riemann solutions between two systems with boundary locally case by case. Based on them, we derive the global $L^1$-estimate between the two solutions by employing the Lipschitz continuous map $\mathcal{P}$ and the local $L^1$-estimates. We further construct an example to show that the convergence rate is optimal.

Authors: Chen, G-QG; Kuang, J; Xiang, W; Zhang, Y

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: IOP Publishing
• Journal: Nonlinearity
• Volume: 38
• Issue: 4
• Article number: 045013
• Publication date: 2025-03-13
• Acceptance date: 2025-02-06
• DOI: 10.1088/1361-6544/adb366
• EISSN: 1361-6544
• ISSN: 0951-7715
• Language: English
• Keywords: standard Riemann semigroup; isothermal hypersonic small disturbance equations; hypersonic similarity; optimal convergence rate; large data; straight wedge; BV solutions