Abstract
We consider a free boundary problem for the equation of one-dimensional isentropic motions with density-dependent viscosityμ =bρ β, whereb andβ are positive constants, when the density function connects to a vacuum continuously on the boundary. We prove that there exists a weak solution globally in time, provided that\(\beta< \frac{5}{{37}}\).
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Okada, M. Free boundary problem for one-dimensional motions of compressible gas and vacuum. Japan J. Indust. Appl. Math. 21, 109 (2004). https://doi.org/10.1007/BF03167467
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DOI: https://doi.org/10.1007/BF03167467