2024/11/05 by Mikihiro Fujii, Fujii, Mikihiro, Keiichi Watanabe +1 · 2 citations
Earth and Planetary Sciences · Engineering · #Analysis of PDEs (math.AP) #FOS: Mathematics #Hydraulic Fracturing and Reservoir Analysis #Meteorological Phenomena and Simulations #Seismic Imaging and Inversion Techniques
paper · pdf · doi:10.48550/arxiv.2411.02701
openalex publication_date 2024/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
We consider the compressible Navier--Stokes system with the Coriolis force on the 3D whole space. In this model, the Coriolis force causes the linearized solution to behave like a 4th order dissipative semigroup \ e-tΔ2 \t>0 with slower time decay rates than the heat kernel, which creates difficulties in nonlinear estimates in the low-frequency part and prevents us from constructing the global strong solutions by following the classical method. On account of this circumstance, the existence of unique global strong solutions has been open even in the classical Matsumura--Nishida framework. In this paper, we overcome the aforementioned difficulties and succeed in constructing a unique global strong solution in the framework of scaling critical Besov spaces. Furthermore, our result also shows that the global solution is constructed for arbitrarily large initial data provided that the speed of the rotation is high and the Mach number is low enough by focusing on the dispersive effect due to the mixture of the Coriolis force and acoustic wave.