The vacuum free boundary problem of one-dimensional non-isentropic compressible Navier-Stokes equations with large initial data is investigated in this paper. The fluid is initially assumed to occupy a finite interval and connect to the vacuum continuously at the free boundary, which is often considered in the gas-vacuum interface problem. Using the method of Lagrangian particle path, we derive some point-wise estimates and weighted spatial and time energy estimates for the classical solutions. Then the global existence and uniqueness of classical solutions are shown, and the expanding speed for the free boundary is proved to be finite. The main difficulty of this problem is the degeneracy of the system near the free boundary. Previous results are only for the solutions with low regularity (cf. [G.Q. Chen and M. Kratka, Commun. Partial Differ. Equations. 27 907-943 (2002)]). Published by AIP Publishing.
机构:
Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Phys, Wuhan 430079, Peoples R ChinaCent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Phys, Wuhan 430079, Peoples R China
Wen, Huanyao
Zhu, Changjiang
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Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Phys, Wuhan 430079, Peoples R ChinaCent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Phys, Wuhan 430079, Peoples R China
Zhu, Changjiang
[J].
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES,
2014,
102
(03):
: 498
-
545
机构:
South China Normal Univ, Sch Math Sci, South China Res Ctr Appl Math & Interdisciplinary, Guangzhou 510631, Guangdong, Peoples R ChinaSouth China Normal Univ, Sch Math Sci, South China Res Ctr Appl Math & Interdisciplinary, Guangzhou 510631, Guangdong, Peoples R China
Ding, Shijin
Huang, Bingyuan
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机构:
Hanshan Normal Univ, Sch Math & Stat, Chaozhou 521041, Peoples R ChinaSouth China Normal Univ, Sch Math Sci, South China Res Ctr Appl Math & Interdisciplinary, Guangzhou 510631, Guangdong, Peoples R China
Huang, Bingyuan
Liu, Xiaoling
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South China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R ChinaSouth China Normal Univ, Sch Math Sci, South China Res Ctr Appl Math & Interdisciplinary, Guangzhou 510631, Guangdong, Peoples R China
机构:
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
论文数: 0引用数: 0
h-index: 0
机构:
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
论文数: 0引用数: 0
h-index: 0
机构:
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