The well-posedness of smooth solution to a 3-D simplified Energy-Transport model is discussed in this paper.We prove the local existence, uniqueness, and asymptotic behavior of solution to the equations with hybrid cross-diffusion.The smooth solution convergences to a stationary solution with an exponential rate as time tends to infinity when the initial date is a small perturbation of the stationary solution.
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Liu et al. (2016) studied this question.
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