VANISHING VISCOSITY SOLUTIONS OF THE COMPRESSIBLE EULER EQUATIONS WITH SPHERICAL SYMMETRY AND LARGE INITIAL DATA

作者: Gui-Qiang G. Chen , Gui-Qiang G. Chen , Mikhail Perepelitsa

DOI: 10.1007/S00220-015-2376-Y

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摘要: We are concerned with spherically symmetric solutions of the Euler equations for multidimensional compressible fluids, which motivated by many important physical situations. Various evidences indicate that may blow up near origin at a certain time under some circumstance. The central feature is strengthening waves as they move radially inward. A longstanding open, fundamental problem whether concentration could be formed origin. In this paper, we develop method vanishing viscosity and related estimate techniques approximate solutions, establish convergence to global finite-energy entropy solution isentropic spherical symmetry large initial data. This indicates not in limit, even though density time. To achieve this, first construct smooth appropriate initial-boundary value problems designed terms, pressure function, boundary conditions, then strong equations.

参考文章(28)
PETER LAX, Shock Waves and Entropy Contributions to Nonlinear Functional Analysis#R##N#Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, April 12–14, 1971. pp. 603- 634 ,(1971) , 10.1016/B978-0-12-775850-3.50018-2
Richard Courant, K. O. Friedrichs, Supersonic flow and shock waves ,(1948)
Ding Xiaxi, Chen Gui-Qiang, Luo Peizhu, Convergence of the fractional step Lax-Friedrichs scheme and Godunov scheme for the isentropic system of gas dynamics Communications in Mathematical Physics. ,vol. 121, pp. 63- 84 ,(1989) , 10.1007/BF01218624
Gui-Qiang Chen, Remarks on DiPerna’s paper “Convergence of the viscosity method for isentropic gas dynamics” Proceedings of the American Mathematical Society. ,vol. 125, pp. 2981- 2986 ,(1997) , 10.1090/S0002-9939-97-03946-4
Tetu Makino, Shigeharu Takeno, Initial boundary value problem for the spherically symmetric motion of isentropic gas Japan Journal of Industrial and Applied Mathematics. ,vol. 11, pp. 171- 183 ,(1994) , 10.1007/BF03167220
Ronald J. DiPerna, Convergence of the viscosity method for isentropic gas dynamics Communications in Mathematical Physics. ,vol. 91, pp. 1- 30 ,(1983) , 10.1007/BF01206047
Gui-Qiang Chen, James Glimm, Global solutions to the compressible Euler equations with geometrical structure Communications in Mathematical Physics. ,vol. 180, pp. 153- 193 ,(1996) , 10.1007/BF02101185
G. B. Whitham, Richard G. Fowler, Linear and Nonlinear Waves ,(1974)