×

On the existence of solutions to the Navier-Stokes-Poisson equations of a two-dimensional compressible flow. (English) Zbl 1107.76065

Summary: We consider Navier-Stokes-Poisson equations for compressible, barotropic flow in two space dimensions. We introduce useful tools from the theory of Orlicz spaces. Then we prove the existence of globally defined finite energy weak solutions for the pressure satisfying \(p(\rho)=a\rho \log^{d}(\rho)\) for large \(\rho\). Here \(d>1\) and \(a>0\).

MSC:

76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35Q30 Navier-Stokes equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Mathematical Topics in Fluid Dynamics, Vol. 2: Compressible Models. Oxford Science Publication: Oxford, 1998.
[2] Feireisl, Journal of Mathematical Fluid Mechanics 3 pp 358– (2001)
[3] Erban, Mathematical Methods in the Applied Sciences 26 pp 489– (2003)
[4] . Weak solutions to the Navier–Stokes–Poisson equations, 2004, preprint.
[5] . Theory of Orlicz Spaces. Marcel Dekker: New York, 1991. · Zbl 0724.46032
[6] Sobolev Space. Academic Press: New York, 1975.
[7] Orlicz Spaces and Interpolation. Seminars in Mathematics. Campinas Sp: Brazil, 1989.
[8] . Interpolation Spaces. Springer: Berlin, Heidelberg, New York, 1976. · doi:10.1007/978-3-642-66451-9
[9] Gustavsson, Studia Mathematica 60 pp 33– (1977)
[10] Analytic Semigroups and Optimal Regularity in Parabolic Problems. Birkhäuser: Berlin, 1995. · Zbl 1261.35001 · doi:10.1007/978-3-0348-0557-5
[11] Navier–Stokes Equations (2nd edn). North-Holland: Amsterdam, 1986.
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.