Abstract
We revisit the classical work of Huang-Matsumura-Xin [9] for contact wave of the one-dimensional compressible Navier-Stokes system under the zero mass condition. The large-time asymptotic stability of a contact wave pattern with a uniform convergence rate (1+t)−14 was proved by Huang-Matsumura-Xin. In this paper, Huang-Matsumura-Xin's convergence rate is improved to (1+t)−58ln12(2+t) by using a new Poincaré type inequality and a detailed energy analysis. Our work is motivated by a problem arising in [9].
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