A solution to a general system of Euler equations for a compressible fluid
Abstract
This paper reveals the existence of solutions to a general Euler system without source for a compressible fluid. The method used to solve the system is not the common invariant regions found in literature. In parallel, we will find the smooth global viscous solutions of the system using the maximum principle.
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Plaza C. R., (2011). Sistemas hiperbólicos de leyes de conservación. En preparación. http://www.fenomec.unam.mx/ramon/publications.html
Ávila C.A., Hortúa H.J., and Casta-eda L., (2010). Ecuación de Euler unidimensional. En: Revista colombiana de física, 42, N.3 pp. 252-256.
Bassi. F., and Rebay. S., (1997). High-order accurate discontinuous finite element solution of the 2D Euler equations. In: Journal of computational physics, 138, pp. 251-285. http://dx.doi.org/10.1006/jcph.1997.5454
Chung Chang S., (1995). The method of space-time conservation element and solution element-A new approach for solving the navier-stokes and Euler equations. In: Journal of computational physics, 119, pp. 295-324. http://dx.doi.org/10.1006/jcph.1995.1137
Maldonado W., y Moreira H., 2006. Solving Euler equations: classical methods and the contraction mapping method revisited. En: Revista Brasileira de Economía, 60, N.2, pp. 167-178. http://dx.doi.org/10.1590/S0034-71402006000200004
Evans Lawrence, (1998). Partial differential equation. Vol 19, American Mathematical Society. http://dx.doi.org/10.1090/S0002-9947-98-02100-X
Lu Yuguang, (2002). Hyperbolic conservations laws and the compensated compactos method. 128, Chapman and Hall, New York. http://dx.doi.org/10.1201/9781420035575
Tsuge N., (2008). Global solutions to the compressible Euler equations with gravitational source. In: Journal of hiperbolic differential equations, Vol 5, N.2, pp. 317-346. http://dx.doi.org/10.1142/s0219891608001507
Gui-Qiang G. Chen and Perepelitsa M., (2010). Vanishing viscosity limit of the Navier-Stokes equations for compressible fluid flow. Communications on Pure and Applied Mathematics, 63, N.11 pp. 1469-1504. http://dx.doi.org/10.1002/cpa.20332
Yan, J. Zhixin, C. Ming, T. (2007). Conservations Laws II: Weak Solutions, En: Revista Colombiana de Matemáticas, Vol. 41, pp. 91-106.
Yan, J. Zhixin, C. Ming, T. 2007. Conservations Laws III: Relaxation limit, En: Revista Colombiana de Matemáticas, Vol. 41, Nº 1, pp. 107-115.
Protter M. H., Weinberger H. F., (1999). Maximum principles in differential equations. Ed. Springer.
Landis E. M., (1997). Second order equations of elliptic and parabolic type. American Mathematical Society. Vol. 171.
Yan J., Zhixin C., and Ming T., (2007). Conservations Laws I: Viscosity Solutions, En: Revista Colombiana de Matemáticas, Vol. 41, pp. 81-90.
