Critical regularity issues for the compressible Navier–Stokes system in bounded domains
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We are concerned with the barotropic compressible Navier–Stokes system in a bounded domain of Rd (with d≥2). In a critical regularity setting, we establish local well-posedness for large data with no vacuum and global well-posedness for small perturbations of a stable constant equilibrium state. Our results rely on new maximal regularity estimates—of independent interest—for the semigroup of the Lamé operator, and of the linearized compressible Navier–Stokes equations.
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Mathematische Annalen, Version of Record (VoR), Springer, Berlin u.a., 2022, https://doi.org/10.1007/s00208-022-02501-w