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Generalized Newton-Busemann Law for Two-dimensional Steady Hypersonic-limit Euler Flows Passing Ramps with Skin-frictions

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Abstract

By considering Radon measure solutions for boundary value problems of stationary non-isentropic compressible Euler equations on hypersonic-limit flows passing ramps with frictions on their boundaries, we construct solutions with density containing Dirac measures supported on the boundaries of the ramps, which represent the infinite-thin shock layers under different assumptions on the skin-frictions. We thus derive corresponding generalizations of the celebrated Newton-Busemann law in hypersonic aerodynamics for distributions of drags/lifts on ramps.

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References

  1. Anderson, John D. Jr. Hypersonic and High-Temperature Gas Dynamics, Third edition. AIAA, 2019

  2. Bouchut, F. On zero pressure gas dynamics, Advances in kinetic theory and computing, Ser. Adv. Math. Appl. Sci., 22: 171–190 (1994)

    Article  Google Scholar 

  3. Brenier, Y., Grenier, E. Sticky particles and scalar conservation laws, SIAM J. Numer. Anal., 35(6): 2317–2328 (1998)

    Article  MathSciNet  Google Scholar 

  4. Chen, G.Q., Liu, H. Formation of δ-shocks and vacuum states in the vanishing pressure limit of solutions to the Euler equations for isentropic fluids, SIAM J. Math. Anal., 34(4): 925–938 (2003)

    Article  MathSciNet  Google Scholar 

  5. Chen, S.X. High speed flight and partial differential equations, Chinese Ann. Math. Ser.B, 43(5): 855–868 (2022)

    Article  MathSciNet  Google Scholar 

  6. Courant, R., Friedrichs, K.O. Supersonic flow and shock waves, Interscience Publishers, 1948

  7. E, W.N., Rykov, Yu. G., Sinai, Ya.G. Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics, Commun. Math. Phys., 177: 349–380 (1996)

    Article  MathSciNet  Google Scholar 

  8. Gao, L., Qu, A.F., Yuan H.R. Delta shock as free piston in pressureless Euler flows, Z. Angew. Math. Phys., 73(3): Paper No. 114, 14 pp (2022)

  9. Huang, F.M., Wang, Z. Well posedness for pressureless flow, Comm. Math. Phys., 222(1): 117–146 (2001)

    Article  MathSciNet  Google Scholar 

  10. Hayes, W. D., Probstein, R. F. Hypersonic Inviscid Flow. Dover Publications, 2004

  11. **, Y.J., Qu, A.F., Yuan, H.R. On two-dimensional steady hypersonic-limit Euler flows passing ramps and radon measure solutions of compressible Euler equations, Commun. Math. Sci., 20: 1331–1361 (2022)

    Article  MathSciNet  Google Scholar 

  12. Kuang, J., **ang, W., Zhang, Y.Q. Convergence rate of hypersonic similarity for steady potential flows over two-dimensional Lipschitz wedge, Calc. Var. Partial Differential Equations, 62(3): Paper No. 106, 49 pp (2023)

  13. Li, J.Q., Yang, H.C. Delta-shocks as limits of vanishing viscosity for multidimensional zeropressure gas dynamics, Quart. Appl. Math, 59(2): 315–342 (2001)

    Article  MathSciNet  Google Scholar 

  14. Qu, A.F., Su, X.Y., Yuan, H.R. Infinite-thin shock layer solutions for stationary compressible conical flows and numerical results via Fourier spectral method, preprint, https://doi.org/10.48550/ar**v.2307.01769 (2023)

  15. Qu, A.F., Yuan, H.R. Radon measure solutions for steady compressible Euler equations of hypersonic-limit conical flows and Newton’s sine-squared law, Journal of Differential Equations, 269: 495–522 (2020)

    Article  MathSciNet  Google Scholar 

  16. Qu, A.F., Yuan, H.R. Measure solutions of one-dimensional piston problem for compressible Euler equations of Chaplygin gas, J. Math. Anal. Appl., 481(1): 123486 (2020)

    Article  MathSciNet  Google Scholar 

  17. Qu, A.F., Yuan, H.R., Zhao, Q. High Mach number limit of one-dimensional piston problem for non-isentropic compressible Euler equations: polytropic gas, J. Math. Phy., 61(1): 1–14 (2020)

    Article  MathSciNet  Google Scholar 

  18. Qu, A.F., Yuan, H.R., Zhao, Q. Hypersonic limit of two-dimensional steady compressible Euler flows passing a straight wedge, Z. Angew. Math. Mech., 100(3): e201800225 (2020)

    Article  MathSciNet  Google Scholar 

  19. Sheng, W.C., Zhang, T., The Riemann problem for the transportation equations in gas dynamics, Mem. Amer. Math. Soc., 137: 77pp (1999)

  20. Yang, H.C., Zhang, Y.Y. New developments of delta shock waves and its applications in systems of conservation laws, Journal of Differential Equations, 252(11): 5951–5993 (2012)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China

    Ai-fang Qu

  2. School of Mathematics and Statistics, **’an Jiaotong University, **’an, 710049, China

    Xue-ying Su

  3. School of Mathematical Sciences, Key Laboratory of Mathematics and Engineering Applications (Ministry of Education) & Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200241, China

    Hai-rong Yuan

Authors
  1. Ai-fang Qu
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  2. Xue-ying Su
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  3. Hai-rong Yuan
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Correspondence to Xue-ying Su.

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Additional information

The project is supported by the National Natural Science Foundation of China (No.11871218 and No.12071298) and Science and Technology Commission of Shanghai Municipality (No. 21JC1402500 and No. 22DZ2229014).

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Qu, Af., Su, Xy. & Yuan, Hr. Generalized Newton-Busemann Law for Two-dimensional Steady Hypersonic-limit Euler Flows Passing Ramps with Skin-frictions. Acta Math. Appl. Sin. Engl. Ser. (2024). https://doi.org/10.1007/s10255-024-1087-6

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  • DOI: https://doi.org/10.1007/s10255-024-1087-6

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