Classical solutions to relativistic Burgers equations in FLRW space-times
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We are interested in the classical solutions to the Cauchy problem of relativistic Burgers equations evolving in Friedmann-Lemat tre-Robertson-Walker (FLRW) space-times, which are spatially homogeneous, isotropic expanding or contracting universes. In such kind of space-times, we first derive the relativistic Burgers equations from the relativistic Euler equations by letting the pressure be zero. Then we can show the global existence of the classical solution to the derived equation in the accelerated expanding space-times with small initial data by the method of characteristics when the spacial dimension n = 1 and energy estimate when n ⩾ 2, respectively. Furthermore, we can also show the lifespan of the classical solution by similar methods when the expansion rate of the space-times is not so fast.
KeywordsFLRW space-times relativistic Burgers equations characteristics energy estimate
MSC(2010)53C44 53C21 58J45 35L45
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This work was supported by National Natural Science Foundation of China (Grant Nos. 91630311 and 11701517), Fundamental Research Funds for the Central Universities (Grant No. 2017XZZX007-02) and the Scientific Research Foundation of Zhejiang Sci-Tech University (Grant No. 16062021-Y).
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