# Low Mach Number Limit and Far Field Convergence Rates of Irrotational Flows in Multidimensional Nozzles with an Obstacle Inside

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**Submitted**: 20 January 2022

**Accepted**: 22 September 2022

**Published online**: 24 January 2023

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**Funding:**The research of the second author was supported in part by NSFC grants 11601401 and 11971024. The research of the third author was partially supported by NSFC grants 11971307 and 11631008, Natural Science Foundation of Shanghai grant 21ZR1433300, and Shanghai Science and Technology Commission grant 22XD1421400.

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