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A remark on free boundary problem of 1-D compressible Navier–Stokes equations with density-dependent viscosity

✍ Scribed by Changsheng Dou; Quansen Jiu

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
202 KB
Volume
33
Category
Article
ISSN
0170-4214

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✦ Synopsis

In this paper, we prove the existence and uniqueness of the weak solution of the one-dimensional compressible Navier-Stokes equations with density-dependent viscosity l(q) = q h with h ∈ (0, c / 2], c > 1. The initial data are a perturbation of a corresponding steady solution and continuously contact with vacuum on the free boundary. The obtained results apply for the one-dimensional Siant-Venant model of shallow water and generalize ones in (Arch.

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✍ Shijin Ding; Jinrui Huang; Xiao-e Liu; Huanyao Wen 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 198 KB 👁 1 views

In this paper, we consider the existence of global smooth solutions to 1D compressible isentropic Navier-Stokes equations with density-dependent viscosity and free boundaries. The initial density q 0 ∈ W 1,2n is bounded below away from zero and the initial velocity u 0 ∈ L 2n . The viscosity coeffic