ON SUBSONIC AND SUBSONIC-SONIC FLOWS IN THE INFINITY LONG NOZZLE WITH GENERAL CONSERVATIVES FORCE

doi:10.1016/S0252-9602(17)30035-8

Abstract

Abstract: In this article, we study irrotational subsonic and subsonic-sonic flows with general conservative forces in the infinity long nozzle. For the subsonic case, the varified Bernoulli law leads a modified cut-off system. Because of the local average estimate, conservative forces do not need any decay condition. Afterwards, the subsonic-sonic limit solutions are constructed by taking the extract subsonic solutions as the approximate sequences.

Key words: Steady flow, homentropic, irrotation, subsonic flow, subsonic-sonic limit

Xumin GU, Tian-Yi WANG. ON SUBSONIC AND SUBSONIC-SONIC FLOWS IN THE INFINITY LONG NOZZLE WITH GENERAL CONSERVATIVES FORCE[J].Acta mathematica scientia,Series B, 2017, 37(3): 752-767.

Trendmd

References

[1] Bers L. An existence theorem in two-dimensional gas dynamics. Proc Symposia Appl Math, 1949, 1:41-46
[2] Bers L. Boundary value problems for minimal surfaces with singularities at infinity. Transactions of the American Mathematical Society, 1951, 70(3):465-491
[3] Bers L. Existence and uniqueness of a subsonic flow past a given profile. Communications on Pure and Applied Mathematics, 1954, 7(3):441-504
[4] Bers L. Mathematical aspects of subsonic and transonic gas dynamics. New York:John Wiley & Sons, Inc, 1958
[5] Chen C, Xie C. Existence of steady subsonic Euler flows through infinitely long periodic nozzles. Journal of Differential Equations, 2012, 252(7):4315-4331
[6] Chen C. Subsonic non-isentropic ideal gas with large vorticity in nozzles. Mathematical Methods in the Applied Sciences, 2015
[7] Chen C, Du L, Xie C, et al. Two Dimensional Subsonic Euler Flows Past a Wall or a Symmetric Body. Archive for Rational Mechanics and Analysis, 2016, 221(2):559-602
[8] Chen G Q, Dafermos C M, Slemrod M, et al. On two-dimensional sonic-subsonic flow. Communications in Mathematical Physics, 2007, 271(3):635-647
[9] Chen G Q, Frid H. Divergence-Measure Fields and Hyperbolic Conservation Laws. Archive for Rational Mechanics and Analysis, 1999, 147(2):89-118
[10] Chen G Q, Huang F M, Wang T Y. Subsonic-sonic limit of approximate solutions to multidimensional steady Euler equations. Archive for Rational Mechanics and Analysis, 2016, 219(2):719-740
[11] Courant R, Friedrichs K O. Supersonic flow and shock waves. Springer Science & Business Media, 1999
[12] Dong G C. Nonlinear partial differential equations of second order. American Mathematical Soc, 1991
[13] Dong G, Ou B. Subsonic flows around a body in space. Communications in Partial Differential Equations, 1993, 18(1/2):355-379
[14] Du L, Xin Z, Yan W. Subsonic flows in a multi-dimensional nozzle. Archive for Rational Mechanics and Analysis, 2011, 201(3):965-1012
[15] Du L, Xie C, Xin Z. Steady subsonic ideal flows through an infinitely long nozzle with large vorticity. Communications in Mathematical Physics, 2014, 328(1):327-354
[16] Duan B, Luo Z. Three-dimensional full Euler flows in axisymmetric nozzles. Journal of Differential Equations, 2013, 254(7):2705-2731
[17] Duan B, Luo Z. Subsonic non-isentropic Euler flows with large vorticity in axisymmetric nozzles. Journal of Mathematical Analysis and Applications, 2015, 430(2):1037-1057
[18] Finn R, Gilbarg D. Asymptotic behavior and uniqueness of plane subsonic flows. Communications on Pure and Applied Mathematics, 1957, 10(1):23-63
[19] Finn R, Gilbarg D. Three-dimensional subsonic flows, and asymptotic estimates for elliptic partial differential equations. Acta Mathematica, 1957, 98(1):265-296
[20] Gilbarg D, Trudinger N S. Elliptic partial differential equations of second order. Springer, 2015
[21] Gu X, Wang T.-Y. On subsonic and subsonic-sonic flows with general conservatives force in exterior domains. Preprint, 2015
[22] Huang F M, Wang T, Wang Y. On multi-dimensional sonic-subsonic flow. Acta Mathematica Scientia, 2011, 31(6):2131-2140
[23] Liu L, Yuan H. Steady subsonic potential flows through infinite multi-dimensional largely-open nozzles. Calculus of Variations and Partial Differential Equations, 2014, 49(1/2):1-36
[24] Frankl F, Keldysh M. Die ussere neumannshe aufgabe fr nichtlineare elliptische differentialgleichungen mit anwendung auf die theorie der flugel im kompressiblen gas. Bull Acad Sci, 1934, 12:561-687
[25] Shiffman M. On the existence of subsonic flows of a compressible fluid. Proceedings of the National Academy of Sciences, 1952, 38(5):434-438
[26] Shiffman M. On the existence of subsonic flows of a compressible fluid. J Rational Mech Anal, 1952, 1:605-652
[27] Xie C, Xin Z. Global subsonic and subsonic-sonic flows through infinitely long nozzles. Indiana University Mathematics Journal, 2007, 56(6):2991-3024
[28] Xie C, Xin Z. Global subsonic and subsonic-sonic flows through infinitely long axially symmetric nozzles. Journal of Differential Equations, 2010, 248(11):2657-2683
[29] Xie C, Xin Z. Existence of global steady subsonic Euler flows through infinitely long nozzles. SIAM Journal on Mathematical Analysis, 2010, 42(2):751-784