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

Dong, Jianwei ; Zhu, Junhui ; Zhang, Litao

Czechoslovak Mathematical Journal, Tome 74 (2024) no. 1, pp. 29-43

Abstract (VO)

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.

Détail

DOI : 10.21136/CMJ.2023.0196-22

Classification : 35B44, 35Q35
Keywords: micoropolar fluid; global classical solution; non-existence

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