Decay of a model system of radiating gas |
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| Authors: | Wenjun Wang Weike Wang Zhigang Wu |
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| Institution: | 1. College of Science, University of Shanghai for Science and Technology, , Shanghai 200093, China;2. Department of Mathematics, Shanghai Jiao Tong University, , Shanghai 200240, China;3. Department of Mathematics, Donghua University, , Shanghai 201620, China |
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| Abstract: | This paper concerns the Cauchy problem of a model system to the radiating gas in  . Large time behaviors of classical solutions to the Cauchy problem are studied without needing the smallness assumption of initial perturbation in L1‐norm. We obtain the optimal HN‐norm time‐decay rates of the solutions in  with 1 ≤ n ≤ 4 by applying the Fourier splitting method introduced by Schonbek (1980) with a slight modification and an energy method. Furthermore, when initial perturbation is bounded in Lp‐norm (p ∈ (1,2]), optimal Lp‐ L2 decay estimates of the derivatives of solutions are shown. Copyright © 2013 John Wiley & Sons, Ltd. |
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| Keywords: | the radiating gas Fourier splitting method negative Sobolev space optimal time‐decay rate |
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