Articles

NONLINEAR STABILITY OF RAREFACTION WAVES FOR A COMPRESSIBLE MICROPOLAR FLUID MODEL WITH ZERO HEAT CONDUCTIVITY

  • Jing JIN ,
  • Noor REHMAN ,
  • Qin JIANG
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  • 1. School of Mathematics and Statistics, Huanggang Normal University, Huanggang 438000, China;
    2. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

Received date: 2018-12-11

  Revised date: 2020-05-12

  Online published: 2020-11-04

Supported by

The first author was supported by Hubei Natural Science (2019CFB834 ). The second author was supported by the NSFC (11971193 ).

Abstract

In 2018, Duan [1] studied the case of zero heat conductivity for a one-dimensional compressible micropolar fluid model. Due to the absence of heat conductivity, it is quite difficult to close the energy estimates. He considered the far-field states of the initial data to be constants; that is, $\lim\limits_{x\rightarrow \pm\infty}(v_0,u_0,\omega_0,\theta_0)(x)=(1,0,0,1)$. He proved that the solution tends asymptotically to those constants. In this article, under the same hypothesis that the heat conductivity is zero, we consider the far-field states of the initial data to be different constants - that is, $\lim\limits_{x\rightarrow \pm\infty}(v_0,u_0,\omega_0,\theta_0)(x)=(v_\pm, u_\pm, 0, \theta_\pm)$-and we prove that if both the initial perturbation and the strength of the rarefaction waves are assumed to be suitably small, the Cauchy problem admits a unique global solution that tends time - asymptotically toward the combination of two rarefaction waves from different families.

Cite this article

Jing JIN , Noor REHMAN , Qin JIANG . NONLINEAR STABILITY OF RAREFACTION WAVES FOR A COMPRESSIBLE MICROPOLAR FLUID MODEL WITH ZERO HEAT CONDUCTIVITY[J]. Acta mathematica scientia, Series B, 2020 , 40(5) : 1352 -1390 . DOI: 10.1007/s10473-020-0512-z

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