2024/10/17 by Pengcheng Mu, Mu, Pengcheng · 1 citation
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.2410.13468
openalex publication_date 2024/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider the low Mach and Rossby number singular limits and longtime existence of strong solution to the initial value problem of 3D compressible rotating Euler equations with ill-prepared initial data. We establish the Strichartz decay estimates that are uniform to the Mach number, the Rossby number, and the ratio of these two parameters for the associated linear propagator without any restrictions on the frequency. In particular, difficulties arisen from the degeneracy of the phase function and the vanishing of the ratio of the two parameters are addressed by elaborately designed splitting techniques and discussions for each frequencies. Using the decay estimates, we prove the longtime existence and obtain a rate of convergence to zero of strong solution to the compressible rotating Euler equations with initial data of finite energy in ℝ3.