Smooth symmetric transonic isothermal flows with nonzero angular velocity. (English) Zbl 1531.35244
Summary: In this paper, the steady inviscid flows with radial symmetry for the isothermal Euler system are studied in an annulus. We present a complete classification of transonic radially symmetric flow patterns in term of physical boundary conditions at the inner and outer circle. By solving the one side boundary problem, we obtain that there exist accelerating or decelerating smooth transonic flows in an annulus. Moreover, the structural stability of these smooth symmetric transonic flows with nonzero angular velocity are further investigated. Furthermore, we examine the transonic solutions with shocks as well via prescribing suitable boundary conditions on the inner and outer circle.
©2023 American Institute of Physics
©2023 American Institute of Physics
MSC:
| 35Q31 | Euler equations |
| 76H05 | Transonic flows |
| 35L65 | Hyperbolic conservation laws |
| 76N15 | Gas dynamics (general theory) |
| 76G25 | General aerodynamics and subsonic flows |
References:
| [1] | Courant, R.; Friedrichs, K. O., Supersonic Flow and Shock Waves (1948), Interscience Publishers Inc.: Interscience Publishers Inc., New York · Zbl 0041.11302 |
| [2] | Weng, S.; Xin, Z.; Yuan, H., Steady compressible radially symmetric flows with nonzero angular velocity in an annulus, J. Differ. Equations, 286, 433-454 (2021) · Zbl 1462.76124 · doi:10.1016/j.jde.2021.03.028 |
| [3] | Weng, S.; Xin, Z.; Yuan, H., On some smooth symmetric transonic flows with nonzero angular velocity and vorticity, Math. Models Methods Appl. Sci., 31, 13, 2773-2817 (2021) · Zbl 1490.76122 · doi:10.1142/s0218202521500615 |
| [4] | Bers, L., Mathematical Aspects of Subsonic and Transonic Gas Dynamics (1958), Wiley: Wiley, New York · Zbl 0083.20501 |
| [5] | Wang, C.; Xin, Z., On a degenerate free boundary problem and continuous subsonic-sonic flows in a convergent nozzle, Arch. Ration. Mech. Anal., 208, 3, 911-975 (2013) · Zbl 1286.35209 · doi:10.1007/s00205-012-0607-3 |
| [6] | Wang, C.; Xin, Z., On sonic curves of smooth subsonic-sonic and transonic flows, SIAM J. Math. Anal., 48, 4, 2414-2453 (2016) · Zbl 1410.76137 · doi:10.1137/16m1056407 |
| [7] | Wang, C.; Xin, Z., Smooth transonic flows of Meyer type in de Laval nozzles, Arch. Ration. Mech. Anal., 232, 3, 1597-1647 (2019) · Zbl 1414.35176 · doi:10.1007/s00205-018-01350-9 |
| [8] | Wang, C.; Xin, Z., Regular subsonic-sonic flows in general nozzles, Adv. Math., 380, 107578 (2021) · Zbl 1458.35321 · doi:10.1016/j.aim.2021.107578 |
| [9] | Chen, G.; Huang, F.; Wang, T., Subsonic-sonic limit of approximate solutions to multidimensional steady Euler equations, Arch. Ration. Mech. Anal., 219, 719-740 (2016) · Zbl 1333.35168 · doi:10.1007/s00205-015-0905-7 |
| [10] | Xie, C.; Xin, Z., Global subsonic and subsonic-sonic flows through infinitely long nozzles, Indiana Univ. Math. J., 56, 2991-3024 (2007) · Zbl 1156.35076 · doi:10.1512/iumj.2007.56.3108 |
| [11] | Xie, C.; Xin, Z., Global subsonic and subsonic-sonic flows through infinitely long axially symmetric nozzles, J. Differ. Equations, 248, 11, 2657-2683 (2010) · Zbl 1193.35143 · doi:10.1016/j.jde.2010.02.007 |
| [12] | Chen, G.; Dafermos, C.; Slemrod, M.; Wang, D., On two-dimensional sonic-subsonic flow, Commun. Math. Phys., 271, 3, 635-647 (2007) · Zbl 1128.35070 · doi:10.1007/s00220-007-0211-9 |
| [13] | Feimin, H.; Wang, T.; Wang, Y., On multi-dimensional sonic-subsonic flow, Acta Math. Sin., 31, 6, 2131-2140 (2011) · Zbl 1265.76039 · doi:10.1016/s0252-9602(11)60389-5 |
| [14] | Zhouping, X.; Shangkun, W., A deformation-curl decomposition for three dimensional steady Euler equations, Sci. Sin. Math., 49, 307-320 (2019) · Zbl 1499.35490 · doi:10.1360/n012018-00125 |
| [15] | Weng, S., A deformation-curl-Poisson decomposition to the three dimensional steady Euler-Poisson system with applications, J. Differ. Equations, 267, 11, 6574-6603 (2019) · Zbl 1425.35038 · doi:10.1016/j.jde.2019.07.002 |
| [16] | Xin, Z.; Yin, H., The transonic shock in a nozzle, 2-D and 3-D complete Euler systems, J. Differ. Equations, 245, 4, 1014-1085 (2008) · Zbl 1165.35031 · doi:10.1016/j.jde.2008.04.010 |
| [17] | Xin, Z.; Yin, H., Transonic shock in a nozzle I: 2D case, Commun. Pure Appl. Math., 58, 8, 999-1050 (2005) · Zbl 1076.76043 · doi:10.1002/cpa.20025 |
| [18] | Li, J.; Xin, Z.; Yin, H., A free boundary value problem for the full Euler system and 2-D transonic shock in a large variable nozzle, Math. Res. Lett., 16, 777-796 (2009) · Zbl 1194.35517 · doi:10.4310/mrl.2009.v16.n5.a3 |
| [19] | Li, J.; Xin, Z.; Yin, H., On transonic shocks in a conic divergent nozzle with axi-symmetric exit pressures, J. Differ. Equations, 248, 423-469 (2010) · Zbl 1191.35179 · doi:10.1016/j.jde.2009.09.017 |
| [20] | Weng, S.; Xie, C.; Xin, Z., Structural stability of the transonic shock problem in a divergent three-dimensional axisymmetric perturbed nozzle, SIAM J. Math. Anal., 53, 279-308 (2021) · Zbl 1464.35159 · doi:10.1137/20m1318869 |
| [21] | Weng, S.; Zhang, Z., Two dimensional subsonic and subsonic-sonic spiral flows outside a porous body, Acta Math. Sci., 42, 4, 1569-1584 (2022) · Zbl 1499.35104 · doi:10.1007/s10473-022-0416-1 |
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