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Globally hyperbolic moment model of arbitrary order for the three-dimensional special relativistic Boltzmann equation with the Anderson-Witting collision

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Abstract

This paper continues to derive the globally hyperbolic moment model of arbitrary order for the three-dimensional special relativistic Boltzmann equation with the Anderson-Witting collision. The method is the model reduction by the operator projection. Finding an orthogonal basis of the weighted polynomial space is crucial and built on infinite families of the complicate relativistic Grad type orthogonal polynomials depending on a parameter and the real spherical harmonics instead of the irreducible tensors. We study the properties of those functions carefully, including their recurrence relations, their derivatives with respect to the independent variable and parameter, and the zeros of the orthogonal polynomials. Our moment model is proved to be globally hyperbolic and linearly stable. Moreover, the Lorentz-covariance and the quasi-one-dimensional case, the non-relativistic and ultra-relativistic limits are also studied.

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Acknowledgements

This work was supported by the Special Project on High-performance Computing under the National Key R&D Program (Grant No. 2016YFB0200603), the Science Challenge Project (Grant No. TZ2016002), the Sino-German Research Group Project (Grant No. GZ 1465) and National Natural Science Foundation of China (Grant Nos. 91630310 and 11421101).

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Authors and Affiliations

  1. Center for Applied Physics and Technology, HEDPS and LMAM, School of Mathematical Sciences, Peking University, Bei**g, 100871, China

    Yangyu Kuang & Huazhong Tang

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  1. Yangyu Kuang
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  2. Huazhong Tang
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Correspondence to Huazhong Tang.

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Kuang, Y., Tang, H. Globally hyperbolic moment model of arbitrary order for the three-dimensional special relativistic Boltzmann equation with the Anderson-Witting collision. Sci. China Math. 65, 1029–1064 (2022). https://doi.org/10.1007/s11425-019-1771-7

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