The well-posedness theory for Euler–Poisson fluids with non-zero heat conduction
2014 ◽
Vol 11
(04)
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pp. 679-703
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This paper is devoted to the Euler–Poisson equations for fluids with non-zero heat conduction, arising in semiconductor science. Due to the thermal effect of the temperature equation, the local well-posedness theory by Xu and Kawashima (2014) for generally symmetric hyperbolic systems in spatially critical Besov spaces does not directly apply. To deal with this difficulty, we develop a generalized version of the Moser-type inequality by using Bony's decomposition. With a standard iteration argument, we then establish the local well-posedness of classical solutions to the Cauchy problem for intial data in spatially Besov spaces.
2008 ◽
Vol 340
(2)
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pp. 1326-1335
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2000 ◽
Vol 09
(01)
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pp. 13-34
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2015 ◽
Vol 13
(2)
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pp. 327-345
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2012 ◽
Vol 2012
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pp. 1-29
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2009 ◽
Vol 12
(2)
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pp. 280-292
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