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 pi(rho) = rho(theta) with 0 is an element of (0, gamma/2], gamma > 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. Rational Mech. Anal. 2006; 182: 223-253). Copyright (C) 2009 John Wiley & Sons, Ltd.
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S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R ChinaCent China Normal Univ, Hubei Key Lab Math Phys, Lab Nonlinear Anal, Sch Math & Stat, Wuhan 430079, Peoples R China
Ding, Shijin
Wen, Huanyao
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Cent China Normal Univ, Hubei Key Lab Math Phys, Lab Nonlinear Anal, Sch Math & Stat, Wuhan 430079, Peoples R China
S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R ChinaCent China Normal Univ, Hubei Key Lab Math Phys, Lab Nonlinear Anal, Sch Math & Stat, Wuhan 430079, Peoples R China
Wen, Huanyao
Zhu, Changjiang
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Cent China Normal Univ, Hubei Key Lab Math Phys, Lab Nonlinear Anal, Sch Math & Stat, Wuhan 430079, Peoples R ChinaCent China Normal Univ, Hubei Key Lab Math Phys, Lab Nonlinear Anal, Sch Math & Stat, Wuhan 430079, Peoples R China
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S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R ChinaS China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China
Ding, Shijin
Huang, Jinrui
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S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R ChinaS China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China
Huang, Jinrui
Liu, Xiao-e
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S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R ChinaS China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China
Liu, Xiao-e
Wen, Huanyao
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S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R ChinaS China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China
机构:
Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100080, Peoples R ChinaChinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China
Huang, Xiangdi
Meng, Weili
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Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100080, Peoples R ChinaChinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China
Meng, Weili
Ni, Anchun
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Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100080, Peoples R ChinaChinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China
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North China Univ Water Resources & Elect Power, Coll Math & Informat Sci, Zhengzhou 450011, Peoples R China
Chinese Acad Sci, Inst Atmospher Phys, Beijing 100029, Peoples R ChinaNorth China Univ Water Resources & Elect Power, Coll Math & Informat Sci, Zhengzhou 450011, Peoples R China
Lian, Ruxu
Liu, Jian
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Quzhou Univ, Coll Teacher Educ, Quzhou 324000, Peoples R ChinaNorth China Univ Water Resources & Elect Power, Coll Math & Informat Sci, Zhengzhou 450011, Peoples R China