THE PROBLEM FOR THE SUPERSONIC PLANE FLOW PAST A CURVED WEDGE

doi:10.1016/S0252-9602(15)30013-8

数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (3): 681-689.doi: 10.1016/S0252-9602(15)30013-8

THE PROBLEM FOR THE SUPERSONIC PLANE FLOW PAST A CURVED WEDGE

王丽

Department of Mathematics and Physics, Shanghai Dianji University, Shanghai 201306, China

收稿日期:2014-04-30 修回日期:2014-07-30 出版日期:2015-05-01 发布日期:2015-05-01
基金资助:
Supported by the TianYuan Special Funds of the National Natural Science Foundation of China (11226171), discipline construction of equipment manufacturing system optimization calculation (13XKJC01), NSFC Project 11101375, and Natural Science Foundation of Zhejiang Province under Grant (LY14A010010).

THE PROBLEM FOR THE SUPERSONIC PLANE FLOW PAST A CURVED WEDGE

Li WANG

Department of Mathematics and Physics, Shanghai Dianji University, Shanghai 201306, China

Received:2014-04-30 Revised:2014-07-30 Online:2015-05-01 Published:2015-05-01
Supported by:
Supported by the TianYuan Special Funds of the National Natural Science Foundation of China (11226171), discipline construction of equipment manufacturing system optimization calculation (13XKJC01), NSFC Project 11101375, and Natural Science Foundation of Zhejiang Province under Grant (LY14A010010).

摘要/Abstract

摘要：

The problem for the supersonic plane flow described by TSD equation past a curved wedge is considered. For a given curved wedge, we will determine the corresponding shock and the solution behind the shock. Moreover, under suitable assumptions, we obtain the global existence and uniqueness for the above mentioned problem.

关键词: TSD equation, shock, free boundary problem

Abstract:

Key words: TSD equation, shock, free boundary problem

中图分类号:

35L65

王丽. THE PROBLEM FOR THE SUPERSONIC PLANE FLOW PAST A CURVED WEDGE[J]. 数学物理学报(英文版), 2015, 35(3): 681-689.

Li WANG. THE PROBLEM FOR THE SUPERSONIC PLANE FLOW PAST A CURVED WEDGE[J]. Acta mathematica scientia,Series B, 2015, 35(3): 681-689.

参考文献

[1] Courant R, Friedrichs K O. Supersonic Flow and Shock Waves. New York: Interscience Publ Inc, 1948
[2] Gu C H. A method for solving the supersonic flow past a curved wedge. Fudan J (Nature Sci), 1962, 7: 11-14
[3] Schaeffer D G. Supersonic flow past a nearly straight wedge. Duke Math J, 1976, 43: 637-670
[4] Li T T. On a free boundary problem. Chinese Ann Math, 1980, 1: 351-358
[5] Chen S X. Asymptotic behavior of supersonic flow past a convex combined wedge. Chinese Annals of Mathematics, 1998, 19: 255-264
[6] Zhang Y Q. Global existence of steady supersonic potential flow past a curvedwedge with a piecewise smoth boundary. SIAM Journal on Mathematical Analysis, 1999, 31: 166-183
[7] Hu D. Global existecce of shock for the supersonic Euler flow past a curved 2-D wedge. Journal of Differential Equation, 2013, 254(5): 2076-2127
[8] Yin H C. Global existence of a shock for the supersonic flow past a curved wedge. Acta Mathematica Sinica, 2006, 22: 1425-1432
[9] Wang L B. Direct problem and inverse problem for the supersonic plane flow past a curved wedge. Math Meth Appl Sci, 2011, 34: 2291-2302
[10] Zhang Y Q. Steady supersonic flow past an almost straight wedge with large vertex angle. J Diff Eqs, 2003, 192: 1-46
[11] Chen G Q, Zhang Y Q, Zhu D W. Existence and stability of supersonic Euler flows past Lipschitz wedges. Arch Rational Mech Anal, 2006, 181: 261-310
[12] Hunter J, Brio M. Weak shock reflection. J Fluid Mech, 2000, 410: 235-261
[13] Wang L. The configuration of shock wave reflection for the TSD equation. Acta Mathematica Sinica, 2013, 29(6): 1131-1158
[14] Li T T, Yu W C. Boundary Value Problems for Quasilinear Hyperbolic Systems//Duke University Math- ematics Series V. Durham: Duke University, 1985
[15] Chen S X. How does a shock in superbolic flow grow out of smooth data? Journal of Mathematical Physics, 2001, 42: 1154-1172

THE PROBLEM FOR THE SUPERSONIC PLANE FLOW PAST A CURVED WEDGE

THE PROBLEM FOR THE SUPERSONIC PLANE FLOW PAST A CURVED WEDGE

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 10

[1]	陈贵强, Matthew RIGBY. STABILITY OF STEADY MULTI-WAVE CONFIGURATIONS FOR THE FULL EULER EQUATIONS OF COMPRESSIBLE FLUID FLOW[J]. 数学物理学报(英文版), 2018, 38(5): 1485-1514.
[2]	K. Divya JOSEPH, P. A. DINESH. INITIAL BOUNDARY VALUE PROBLEM FOR A NONCONSERVATIVE SYSTEM IN ELASTODYNAMICS[J]. 数学物理学报(英文版), 2018, 38(3): 1043-1056.
[3]	唐少君, 张澜. NONLINEAR STABILITY OF VISCOUS SHOCK WAVES FOR ONE-DIMENSIONAL NONISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH A CLASS OF LARGE INITIAL PERTURBATION[J]. 数学物理学报(英文版), 2018, 38(3): 973-1000.
[4]	施小丁, 雍燕, 张英龙. VANISHING VISCOSITY FOR NON-ISENTROPIC GAS DYNAMICS WITH INTERACTING SHOCKS[J]. 数学物理学报(英文版), 2016, 36(6): 1699-1720.
[5]	吴法, 戴晖辉, 孔德兴. MECHANISM FOR THE TRANSITION FROM A REGULAR REFLECTION TO A MACH REFLECTION OR A VON NEUMANN REFLECTION[J]. 数学物理学报(英文版), 2016, 36(3): 931-944.
[6]	何躏, 唐少君, 王涛. STABILITY OF VISCOUS SHOCK WAVES FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY[J]. 数学物理学报(英文版), 2016, 36(1): 34-48.
[7]	Volker ELLING. RELATIVE ENTROPY AND COMPRESSIBLE POTENTIAL FLOW[J]. 数学物理学报(英文版), 2015, 35(4): 763-776.
[8]	唐平凡\|方北香\|王亚光. ON LOCAL STRUCTURAL STABILITY OF ONE-DIMENSIONAL SHOCKS IN RADIATION HYDRODYNAMICS[J]. 数学物理学报(英文版), 2015, 35(1): 1-44.
[9]	Helmer A. FRIIS, Steinar EVJE. WELL-POSEDNESS OF A COMPRESSIBLE GAS-LIQUID MODEL FOR DEEPWATER OIL WELL OPERATIONS[J]. 数学物理学报(英文版), 2014, 34(1): 107-124.
[10]	陈正争, 肖清华. NONLINEAR STABILITY OF PLANAR SHOCK PROFILES FOR THE GENERALIZED KdV-BURGERS EQUATION IN SEVERAL DIMENSIONS[J]. 数学物理学报(英文版), 2013, 33(6): 1531-1550.
[11]	王振, 张庆玲. THE RIEMANN PROBLEM WITH DELTA INITIAL DATA FOR THE ONE-DIMENSIONAL CHAPLYGIN GAS EQUATIONS[J]. 数学物理学报(英文版), 2012, 32(3): 825-841.
[12]	Hakho Hong, Feimin Huang. ASYMPTOTIC BEHAVIOR OF SOLUTIONS TOWARD THE SUPERPOSITION OF CONTACT DISCONTINUITY AND SHOCK WAVE FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY[J]. 数学物理学报(英文版), 2012, 32(1): 389-412.
[13]	Govind Menon. LESSER KNOWN MIRACLES OF BURGERS EQUATION[J]. 数学物理学报(英文版), 2012, 32(1): 281-294.
[14]	王振, 张庆玲. SPIRAL SOLUTION TO THE TWO-DIMENSIONAL TRANSPORT EQUATIONS[J]. 数学物理学报(英文版), 2010, 30(6): 2110-2128.
[15]	Blake Barker, Olivier Lafitte, Kevin Zumbrun. EXISTENCE AND STABILITY OF VISCOUS SHOCK PROFILES FOR 2-D ISENTROPIC MHD WITH INFINITE ELECTRICAL RESISTIVITY[J]. 数学物理学报(英文版), 2010, 30(2): 447-498.