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Nonlinear Stability of Rarefaction Waves for a Compressible Micropolar Fluid Model with Zero Heat Conductivity

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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, \(\mathop {\lim }\limits_{x \to \pm \infty } ({v_0},{u_0},{\omega _0},{\theta _0})(x) = (1,0,0,1)\). 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, \(\mathop {\lim }\limits_{x \to \pm \infty } ({v_0},{u_0},{\omega _0},{\theta _0})(x) = ({v_ \pm },{u_ \pm },0,{\theta _ \pm })\)-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.

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Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Huanggang Normal University, Huanggang, 438000, China

    Jing Jin & Qin Jiang

  2. School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China

    Noor Rehman

Authors
  1. Jing Jin
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  2. Noor Rehman
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  3. Qin Jiang
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Corresponding author

Correspondence to Jing Jin.

Additional information

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

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Jin, J., Rehman, N. & Jiang, Q. Nonlinear Stability of Rarefaction Waves for a Compressible Micropolar Fluid Model with Zero Heat Conductivity. Acta Math Sci 40, 1352–1390 (2020). https://doi.org/10.1007/s10473-020-0512-z

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  • DOI: https://doi.org/10.1007/s10473-020-0512-z

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