Abstract
This paper is concerned with the exponential stability in H 1 and H 2 of global weak solutions to the compressible Navier–Stokes equations with the cylinder symmetry in R 3 when the initial total energy is sufficiently small. Such a circular coaxial cylinder symmetric domain in R 3 is an unbounded domain, but under our assumptions on the solutions depending only on one radial spatial variable r ∈ G = { r ∈ R + , 0 < a < r < b < + ∞ } , the related domain G to equations is a bounded domain. The Matsumura and Nishida result in R 3 requires the smallness of initial data, while our result does not need the smallness of density.
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