Non-existence of global classical solutions to 1D compressible heat-conducting micropolar fluid

We study the non-existence of global classical solutions to 1D compressible heat-conducting micropolar fluid without viscosity. We first show that the life span of the classical solutions with decay at far fields must be finite for the 1D Cauchy problem if the initial momentum weight is positive. Th...

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Bibliographic Details
Published in:Czechoslovak mathematical journal 2024-04, Vol.74 (1), p.29-43
Main Authors: Dong, Jianwei, Zhu, Junhui, Zhang, Litao
Format: Article
Language:English
Subjects:
Analysis
Boundary value problems
Cauchy problems
Compressibility
Convex and Discrete Geometry
Heat transfer
Heat transmission
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Micropolar fluids
Ordinary Differential Equations
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Summary:We study the non-existence of global classical solutions to 1D compressible heat-conducting micropolar fluid without viscosity. We first show that the life span of the classical solutions with decay at far fields must be finite for the 1D Cauchy problem if the initial momentum weight is positive. Then, we present several sufficient conditions for the non-existence of global classical solutions to the 1D initial-boundary value problem on [0, 1]. To prove these results, some new average quantities are introduced.
ISSN:0011-4642
1572-9141
DOI:10.21136/CMJ.2023.0196-22