Abstract
We consider the low Mach number limit problem of the Euler equations for isentropic fluids in the analytic spaces. We prove that, given general analytic initial data, the solution is uniformly bounded on a time interval independent of the small parameter and the incompressible limit holding in the analytic norm. The same results extend more generally to Gevrey initial data with convergence holds in a Gevrey norm. The results extend the isentropic fluids in Jang et al. (J Differ Equ 299:284–332, 2021) to more general pressure laws.
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Acknowledgements
LL was supported in part by the NSF grants DMS-2009458 and DMS-1907992, while YT was supported in part by the NSF grant DMS-1106853. The authors are grateful to Juhi Jang and Igor Kukavica for fruitful discussions.
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Li, L., Tan, Y. The incompressible limit of the isentropic fluids in the analytic spaces. Z. Angew. Math. Phys. 74, 164 (2023). https://doi.org/10.1007/s00033-023-02059-w
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DOI: https://doi.org/10.1007/s00033-023-02059-w