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Keywords:
micoropolar fluid; global classical solution; non-existence
Summary:
We study the non-existence of global classical solutions to 1D compressible heat-conducting micropolar fluid without viscosity. We first show that the life span of the classical solutions with decay at far fields must be finite for the 1D Cauchy problem if the initial momentum weight is positive. Then, we present several sufficient conditions for the non-existence of global classical solutions to the 1D initial-boundary value problem on $[0,1]$. To prove these results, some new average quantities are introduced.
References:
[1] Bašić-Šiško, A., Dražić, I.: Global solution to a one-dimensional model of viscous and heat-conducting micropolar real gas flow. J. Math. Anal. Appl. 495 (2021), Article ID 124690, 26 pages. DOI 10.1016/j.jmaa.2020.124690 | MR 4172845 | Zbl 1462.35281
[2] Bašić-Šiško, A., Dražić, I.: Uniqueness of generalized solution to micropolar viscous real gas flow with homogeneous boundary conditions. Math. Methods Appl. Sci. 44 (2021), 4330-4341. DOI 10.1002/mma.7032 | MR 4235508 | Zbl 1473.76044
[3] Bašić-Šiško, A., Dražić, I.: Local existence for viscous reactive micropolar real gas flow and thermal explosion with homogeneous boundary conditions. J. Math. Anal. Appl. 509 (2022), Article ID 125988, 31 pages. DOI 10.1016/j.jmaa.2022.125988 | MR 4362867 | Zbl 1509.35207
[4] Bašić-Šiško, A., Dražić, I., Simčić, L.: One-dimensional model and numerical solution to the viscous and heat-conducting micropolar real gas flow with homogeneous boundary conditions. Math. Comput. Simul. 195 (2022), 71-87. DOI 10.1016/j.matcom.2021.12.024 | MR 4372809 | Zbl 07487705
[5] Chang, S., Duan, R.: The limits of coefficients of angular viscosity and microrotation viscosity to one-dimensional compressible Navier-Stokes equations for micropolar fluids model. J. Math. Anal. Appl. 516 (2022), Article ID 126462, 41 pages. DOI 10.1016/j.jmaa.2022.126462 | MR 4450883 | Zbl 1504.35219
[6] Cui, H., Yin, H.: Stationary solutions to the one-dimensional micropolar fluid model in a half line: Existence, stability and convergence rate. J. Math. Anal. Appl. 449 (2017), 464-489. DOI 10.1016/j.jmaa.2016.11.065 | MR 3595213 | Zbl 1360.35172
[7] Dong, J., Ju, Q.: Blow-up of smooth solutions to compressible quantum Navier-Stokes equations. Sci. Sin., Math. 50 (2020), 873-884 Chinese. DOI 10.1360/N012018-00134 | Zbl 1499.35117
[8] Dong, J., Xue, H., Lou, G.: Singularities of solutions to compressible Euler equations with damping. Eur. J. Mech., B, Fluids 76 (2019), 272-275. DOI 10.1016/j.euromechflu.2019.03.005 | MR 3926951 | Zbl 1469.35171
[9] Dong, J., Zhu, J., Wang, Y.: Blow-up for the compressible isentropic Navier-Stokes- Poisson equations. Czech. Math. J. 70 (2020), 9-19. DOI 10.21136/CMJ.2019.0156-18 | MR 4078344 | Zbl 1513.35449
[10] Dong, J., Zhu, J., Xue, H.: Blow-up of smooth solutions to the Cauchy problem for the viscous two-phase model. Math. Phys. Anal. Geom. 21 (2018), Article ID 20, 8 pages. DOI 10.1007/s11040-018-9279-z | MR 3835282 | Zbl 1394.76136
[11] Duan, R.: Global solutions for a one-dimensional compressible micropolar fluid model with zero heat conductivity. J. Math. Anal. Appl. 463 (2018), 477-495. DOI 10.1016/j.jmaa.2018.03.009 | MR 3785466 | Zbl 1390.35267
[12] Duan, R.: Global strong solution for initial-boundary value problem of one-dimensional compressible micropolar fluids with density dependent viscosity and temperature dependent heat conductivity. Nonlinear Anal., Real World Appl. 42 (2018), 71-92. DOI 10.1016/j.nonrwa.2017.12.006 | MR 3773352 | Zbl 1516.35330
[13] Eringen, A. C.: Theory of micropolar fluids. J. Math. Mech. 16 (1966), 1-18. DOI 10.1512/iumj.1967.16.16001 | MR 0204005
[14] Feng, Z., Zhu, C.: Global classical large solution to compressible viscous micropolar and heat-conducting fluids with vacuum. Discrete Contin. Dyn. Syst. 39 (2019), 3069-3097. DOI 10.3934/dcds.2019127 | MR 3959421 | Zbl 1420.35235
[15] Gao, J., Cui, H.: Large-time behavior of solutions to the inflow problem of the non-isentropic micropolar fluid model. Acta Math. Sci., Ser. B, Engl. Ed. 41 (2021), 1169-1195. DOI 10.1007/s10473-021-0410-z | MR 4266912 | Zbl 1513.35452
[16] Huang, L., Yang, X.-G., Lu, Y., Wang, T.: Global attractors for a nonlinear one-dimensional compressible viscous micropolar fluid model. Z. Angew. Math. Phys. 70 (2019), Article ID 40, 20 pages. DOI 10.1007/s00033-019-1083-5 | MR 3908857 | Zbl 1412.35220
[17] Jiu, Q., Wang, Y., Xin, Z.: Remarks on blow-up of smooth solutions to the compressible fluid with constant and degenerate viscosities. J. Differ. Equations 259 (2015), 2981-3003. DOI 10.1016/j.jde.2015.04.007 | MR 3360663 | Zbl 1319.35194
[18] {Ł}ukaszewicz, G.: Micropolar Fluids: Theory and Applications. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Boston (1999). DOI 10.1007/978-1-4612-0641-5 | MR 1711268 | Zbl 0923.76003
[19] Mujaković, N.: One-dimensional flow of a compressible viscous micropolar fluid: A local existence theorem. Glas. Mat., III. Ser. 33 (1998), 71-91. MR 1652788 | Zbl 0912.35135
[20] Mujaković, N.: One-dimensional flow of a compressible viscous micropolar fluid: A global existence theorem. Glas. Mat., III. Ser. 33 (1998), 199-208. MR 1695531 | Zbl 0917.76004
[21] Mujaković, N.: Global in time estimates for one-dimensional compressible viscous micropolar fluid model. Glas. Mat., III. Ser. 40 (2005), 103-120. DOI 10.3336/gm.40.1.10 | MR 2195864 | Zbl 1082.35128
[22] Mujaković, N.: One-dimensional flow of a compressible viscous micropolar fluid: The Cauchy problem. Math. Commun. 10 (2005), 1-14. MR 2239387 | Zbl 1076.35103
[23] Mujaković, N.: Uniqueness of a solution of the Cauchy problem for one-dimensional compressible viscous micropolar fluid model. Appl. Math. E-Notes 6 (2006), 113-118. MR 2219158 | Zbl 1154.76045
[24] Mujaković, N.: Non-homogeneous boundary value problem for one-dimensional compressible viscous micropolar fluid model: A local existence theorem. Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 53 (2007), 361-379. DOI 10.1007/s11565-007-0023-z | MR 2358235 | Zbl 1180.35007
[25] Mujaković, N.: Non-homogeneous boundary value problem for one-dimensional compressible viscous micropolar fluid model: A global existence theorem. Math. Inequal. Appl. 12 (2009), 651-662. DOI 10.7153/mia-12-49 | MR 2540984 | Zbl 1178.35007
[26] Mujaković, N.: 1-D compressible viscous micropolar fluid model with non-homogeneous boundary conditons for temperature: A local existence theorem. Nonlinear Anal., Real World Appl. 13 (2012), 1844-1853. DOI 10.1016/j.nonrwa.2011.12.012 | MR 2891014 | Zbl 1254.76122
[27] Mujaković, N.: The existence of a global solution for one dimensional compressible viscous micropolar fluid with non-homogeneous boundary conditions for temperature. Nonlinear Anal., Real World Appl. 19 (2014), 19-30. DOI 10.1016/j.nonrwa.2014.02.006 | MR 3206655 | Zbl 1300.35100
[28] Mujaković, N., Črnjarić-Žic, N.: Convergent finite difference scheme for 1D flow of compressible micropolar fluid. Int. J. Numer. Anal. Model. 12 (2015), 94-124. MR 3286458 | Zbl 1329.35251
[29] Qin, Y., Wang, T., Hu, G.: The Cauchy problem for a 1D compressible viscous micropolar fluid model: Analysis of the stabilization and the regularity. Nonlinear Anal., Real World Appl. 13 (2012), 1010-1029. DOI 10.1016/j.nonrwa.2010.10.023 | MR 2863933 | Zbl 1239.35127
[30] Sideris, T. C.: Formation of singularities in three-dimensional compressible fluids. Commun. Math. Phys. 101 (1985), 475-485. DOI 10.1007/BF01210741 | MR 0815196 | Zbl 0606.76088
[31] Wang, G., Guo, B., Fang, S.: Blow-up of the smooth solutions to the compressible Navier-Stokes equations. Math. Methods Appl. Sci. 40 (2017), 5262-5272. DOI 10.1002/mma.4384 | MR 3689262 | Zbl 1383.35034
[32] Xin, Z.: Blowup of smooth solutions to the compressible Navier-Stokes equations with compact density. Commun. Pure Appl. Math. 51 (1998), 229-240. DOI 10.1002/(SICI)1097-0312(199803)51:3<229::AID-CPA1>3.0.CO;2-C | MR 1488513 | Zbl 0937.35134
[33] Xin, Z., Yan, W.: On blowup of classical solutions to the compressible Navier-Stokes equations. Commun. Math. Phys. 321 (2013), 529-541. DOI 10.1007/s00220-012-1610-0 | MR 3063918 | Zbl 1287.35059
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