×

Global solution to the exterior problem for spherically symmetric compressible Navier-Stokes equations with density-dependent viscosity and discontinuous initial data. (English) Zbl 1294.35067

Summary: In this paper, we consider the exterior problem for spherically symmetric isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficients and discontinuous initial data. We prove that there exists a unique global piecewise regular solution for piecewise regular initial density with bounded jump discontinuity. In particular, the jump of density decays exponentially in time and the piecewise regular solution tends to the equilibrium state exponentially as \(t \to +\infty\)

MSC:

35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] doi:10.1017/S0308210500018953 · Zbl 0635.35074 · doi:10.1017/S0308210500018953
[2] doi:10.1016/0022-0396(92)90042-L · Zbl 0762.35085 · doi:10.1016/0022-0396(92)90042-L
[3] doi:10.1512/iumj.1992.41.41060 · Zbl 0765.35033 · doi:10.1512/iumj.1992.41.41060
[4] doi:10.1006/jdeq.1995.1111 · Zbl 0836.35120 · doi:10.1006/jdeq.1995.1111
[5] doi:10.1007/BF00390346 · Zbl 0836.76082 · doi:10.1007/BF00390346
[6] doi:10.1080/03605300008821583 · Zbl 0977.35104 · doi:10.1080/03605300008821583
[7] doi:10.1007/s002050050055 · Zbl 0904.76074 · doi:10.1007/s002050050055
[8] doi:10.1016/j.jde.2005.07.011 · Zbl 1357.35245 · doi:10.1016/j.jde.2005.07.011
[9] doi:10.1016/j.jde.2009.11.029 · Zbl 1189.35388 · doi:10.1016/j.jde.2009.11.029
[10] doi:10.1016/j.euromechflu.2006.04.007 · Zbl 1105.76021 · doi:10.1016/j.euromechflu.2006.04.007
[11] doi:10.1137/070680333 · doi:10.1137/070680333
[12] doi:10.1016/S0022-0396(03)00060-3 · Zbl 1025.35020 · doi:10.1016/S0022-0396(03)00060-3
[13] doi:10.1081/PDE-100002385 · Zbl 0982.35084 · doi:10.1081/PDE-100002385
[14] doi:10.1006/jdeq.2001.4140 · Zbl 1003.76073 · doi:10.1006/jdeq.2001.4140
[15] doi:10.1007/s00220-002-0703-6 · Zbl 1045.76038 · doi:10.1007/s00220-002-0703-6
[16] doi:10.1137/060658199 · Zbl 1141.76054 · doi:10.1137/060658199
[17] doi:10.1080/03605302.2010.516785 · Zbl 1228.35138 · doi:10.1080/03605302.2010.516785
[18] doi:10.1007/s00220-008-0495-4 · Zbl 1173.35099 · doi:10.1007/s00220-008-0495-4
[19] doi:10.1007/s00220-011-1334-6 · Zbl 1233.35156 · doi:10.1007/s00220-011-1334-6
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.