2025/04/02 by Xie, Minghong, Xu, Saiguo, Zhang, Yinghui
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2504.01288
This paper investigates the global existence of classical solutions to the isentropic compressible Navier-Stokes equations with slip boundary condition in a three-dimensional (3D) exterior domain. It is shown that the classical solutions with large initial energy and vacuum exist globally in time when the adiabatic exponent γ>1 is sufficiently close to 1 (near-isothermal regime). This constitutes an extension of the celebrated result for the one-dimensional Cauchy problem of the isentropic Euler equations that has been established in 1973 by Nishida and Smoller (Comm. Pure Appl. Math. 26 (1973), 183-200). To the best of our knowledge, we establish the first result on the global existence of large-energy solutions with vacuum to the compressible Navier-Stokes equations with slip boundary condition in a 3D exterior domain, which improves previous related works where either small initial energy is required or boundary effects are ignored.