Abstract In this paper, we establish analyticity of solutions to the barotropic compressible Navier-Stokes equations describing the motion of the density ρ and the velocity field u in R 3 . We assume that ρ 0 is a small perturbation of 1 and ( 1 − 1 / ρ 0 , u 0 ) are analytic in Besov spaces with analyticity radius ω > 0 . We show that the corresponding solutions are analytic globally in time when ( 1 − 1 / ρ 0 , u 0 ) are sufficiently small. To do this, we introduce the exponential operator e ( ω − θ ( t ) ) D acting on ( 1 − 1 / ρ , u ) , where D is the differential operator whose Fourier symbol is given by | ξ | 1 = | ξ 1 | + | ξ 2 | + | ξ 3 | and θ ( t ) is chosen to satisfy θ ( t ) ω globally in time.

中文翻译：

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正压可压缩 Navier-Stokes 方程解的解析性

摘要 在本文中，我们建立了描述R 3 中密度ρ 和速度场u 运动的正压可压缩Navier-Stokes 方程的解的解析性。我们假设 ρ 0 是 1 的小扰动，并且 ( 1 − 1 / ρ 0 , u 0 ) 在解析半径 ω > 0 的 Besov 空间中是解析的。我们表明，当 ( 1 − 1 / ρ 0 , u 0 ) 足够小时，相应的解在时间上是全局解析的。为此，我们引入了作用于 ( 1 − 1 / ρ , u ) 的指数算子 e ( ω − θ ( t ) ) D ，其中 D 是其傅立叶符号由 | 给出的微分算子。ξ | 1 = | ξ 1 | + | ξ 2 | + | ξ 3 | 并且选择 θ ( t ) 以在时间上全局满足 θ ( t ) ω。