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Abstract:
We investigate the thermal instability of a smooth equilibrium state, in which the density function satisfies Schwarzschild's (instability) condition, to a compressible heat-conducting viscous flow without heat conductivity in the presence of a uniform gravitational field in a three-dimensional bounded domain. We show that the equilibrium state is linearly unstable by a modified variational method. Then, based on the constructed linearly unstable solutions and a local well-posedness result of classical solutions to the original nonlinear problem, we further construct the initial data of linearly unstable solutions to be the one of the original nonlinear problem, and establish an appropriate energy estimate of Gronwall-type. With the help of the established energy estimate, we finally show that the equilibrium state is nonlinearly unstable in the sense of Hadamard by a careful bootstrap instability argument.
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JOURNAL OF MATHEMATICAL FLUID MECHANICS
ISSN: 1422-6928
Year: 2018
Issue: 4
Volume: 20
Page: 1509-1539
1 . 5 3 2
JCR@2018
1 . 2 0 0
JCR@2023
ESI Discipline: MATHEMATICS;
ESI HC Threshold:68
JCR Journal Grade:3
CAS Journal Grade:4
Cited Count:
WoS CC Cited Count: 9
SCOPUS Cited Count: 9
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 1
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