Nishida–Smoller‐type large solutions for the compressible Navier–Stokes equations with slip boundary conditions in 3D exterior domains

Abstract This paper establishes the global existence of classical solutions with large initial energy and vacuum to the isentropic compressible Navier–Stokes equations under slip boundary conditions in a three‐dimensional (3D) exterior domain. For a near‐isothermal fluid (the adiabatic exponent sufficiently close to 1) with zero far‐field density (), the solutions are proved to be global. This extends the classical one‐dimensional result of Nishida and Smoller in 1973 (Comm. Pure Appl. Math. 26 (1973), 183–200). It provides the first global existence result for large‐energy solutions with vacuum in a 3D exterior domain with a physical boundary. As a byproduct, for the whole space with , a global result is obtained under a general smallness condition on , relaxing the previous restriction in Hong–Hou–Peng–Zhu (Math. Ann. 388 (2024), no. 2, 2163‐2194).