Xu, Jiang The well-posedness theory for Euler-Poisson fluids with non-zero heat conduction. (English) Zbl 1319.35198 J. Hyperbolic Differ. Equ. 11, No. 4, 679-703 (2014). This paper study the Cauchy problem of the Euler-Poisson equations for fluids with non-zero heat conduction. By developing a generalized Moser-type inequality, the author prove the local well-posedness of classical solutions to the Cauchy problem of the Euler-Poisson equations with non-zero heat conduction, with initial data in spatially Besov spaces. Reviewer: Cheng He (Beijing) MSC: 35Q35 PDEs in connection with fluid mechanics 35M10 PDEs of mixed type 76X05 Ionized gas flow in electromagnetic fields; plasmic flow 80A20 Heat and mass transfer, heat flow (MSC2010) 82D37 Statistical mechanics of semiconductors Keywords:Euler-Poisson equations; semi-conductor; classical solution; local well-posedness; Besov space PDFBibTeX XMLCite \textit{J. Xu}, J. Hyperbolic Differ. Equ. 11, No. 4, 679--703 (2014; Zbl 1319.35198) Full Text: DOI References: [1] DOI: 10.4171/RMI/505 · Zbl 1175.35099 · doi:10.4171/RMI/505 [2] DOI: 10.1137/S0036141099355174 · Zbl 0984.35104 · doi:10.1137/S0036141099355174 [3] DOI: 10.1006/jmaa.2000.7359 · Zbl 0982.35112 · doi:10.1006/jmaa.2000.7359 [4] DOI: 10.1007/978-3-642-16830-7 · Zbl 1227.35004 · doi:10.1007/978-3-642-16830-7 [5] DOI: 10.1007/BF02791256 · Zbl 0938.35125 · doi:10.1007/BF02791256 [6] DOI: 10.1006/jdeq.1995.1131 · Zbl 0878.35089 · doi:10.1006/jdeq.1995.1131 [7] G. Q. Chen, J. W. Jerome and B. Zhang, Modeling and Computation for Application in Mathematics, Science, and Engineering (Oxford University Press, New York, 1998) pp. 189–215. [8] DOI: 10.1007/s002220000078 · Zbl 0958.35100 · doi:10.1007/s002220000078 [9] DOI: 10.1081/PDE-100106132 · Zbl 1007.35071 · doi:10.1081/PDE-100106132 [10] DOI: 10.1007/BF01765842 · Zbl 0808.35150 · doi:10.1007/BF01765842 [11] DOI: 10.1090/S0002-9947-04-03526-3 · Zbl 1052.35014 · doi:10.1090/S0002-9947-04-03526-3 [12] Gamba I., Comm. Partial Differential Equations 17 pp 553– (1992) [13] Gasser I., Quart. Appl. Math. 57 pp 269– (1999) · Zbl 1034.82067 · doi:10.1090/qam/1686190 [14] DOI: 10.1007/s00205-005-0369-2 · Zbl 1148.82030 · doi:10.1007/s00205-005-0369-2 [15] DOI: 10.1007/s00605-002-0485-0 · Zbl 1004.82018 · doi:10.1007/s00605-002-0485-0 [16] DOI: 10.1142/S0218202502001891 · Zbl 1174.82349 · doi:10.1142/S0218202502001891 [17] DOI: 10.1007/BF00280740 · Zbl 0343.35056 · doi:10.1007/BF00280740 [18] DOI: 10.1016/j.jde.2006.01.001 · Zbl 1093.76066 · doi:10.1016/j.jde.2006.01.001 [19] DOI: 10.1007/978-1-4612-1116-7 · doi:10.1007/978-1-4612-1116-7 [20] DOI: 10.1007/BF01168147 · Zbl 0617.35078 · doi:10.1007/BF01168147 [21] DOI: 10.1007/BF00379918 · Zbl 0829.35128 · doi:10.1007/BF00379918 [22] DOI: 10.1006/jdeq.1999.3676 · Zbl 0987.35103 · doi:10.1006/jdeq.1999.3676 [23] DOI: 10.1007/978-3-7091-6961-2 · doi:10.1007/978-3-7091-6961-2 [24] DOI: 10.1007/s00205-008-0129-1 · Zbl 1166.82020 · doi:10.1007/s00205-008-0129-1 [25] DOI: 10.1017/S0308210500004856 · Zbl 1123.35009 · doi:10.1017/S0308210500004856 [26] DOI: 10.1515/9783110812411 · doi:10.1515/9783110812411 [27] DOI: 10.1006/jdeq.1997.3377 · Zbl 0914.35102 · doi:10.1006/jdeq.1997.3377 [28] DOI: 10.3934/cpaa.2009.8.1073 · Zbl 1158.35392 · doi:10.3934/cpaa.2009.8.1073 [29] DOI: 10.1142/S0218202510004489 · Zbl 1195.35034 · doi:10.1142/S0218202510004489 [30] DOI: 10.1016/j.jde.2011.09.040 · Zbl 1242.35184 · doi:10.1016/j.jde.2011.09.040 [31] DOI: 10.1007/s00205-013-0679-8 · Zbl 1293.35173 · doi:10.1007/s00205-013-0679-8 [32] DOI: 10.3934/dcds.2009.25.1319 · Zbl 1180.35059 · doi:10.3934/dcds.2009.25.1319 [33] DOI: 10.5802/aif.2033 · Zbl 1097.35118 · doi:10.5802/aif.2033 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.