Blowup criterion for the Cauchy problem of 2D compressible viscous micropolar fluids with vacuum

Dayong Huang; Guoliang Hou; Dayong Huang; Guoliang Hou

doi:10.3934/math.20241268

AIMS Mathematics

2024, Volume 9, Issue 9: 25956-25965. doi: 10.3934/math.20241268

Previous Article Next Article

Research article

Blowup criterion for the Cauchy problem of 2D compressible viscous micropolar fluids with vacuum

Dayong Huang ^,,
Guoliang Hou

College of Mathematics, Changchun Normal University, Changchun, China

Received: 19 July 2024 Revised: 29 August 2024 Accepted: 03 September 2024 Published: 06 September 2024
MSC : 76N10, 35Q35, 35B40, 35D35

In this study, we establish a regular criterion for the 2D compressible micropolar viscous fluids with vacuum that is independent of the velocity of rotation of the microscopic particles. Specifically, we show that if the density verifies $ \|\rho\|_{L^\infty(0, T; L^\infty)} < \infty $, then the strong solution will exist globally on $ \Bbb R^2\times(0, T) $. Consequently, we generalize the results of Zhong (Discrete Contin. Dyn. Syst. Ser. B, 25 (2020), no. 12, 4603–4615) to the compressible case. In particular, we don't need the additional compatibility condition.
- compressible micropolar fluids,
- strong solutions,
- vacuum,
- Cauchy problem,
- blowup criterion
Citation: Dayong Huang, Guoliang Hou. Blowup criterion for the Cauchy problem of 2D compressible viscous micropolar fluids with vacuum[J]. AIMS Mathematics, 2024, 9(9): 25956-25965. doi: 10.3934/math.20241268

Related Papers:

Abstract

In this study, we establish a regular criterion for the 2D compressible micropolar viscous fluids with vacuum that is independent of the velocity of rotation of the microscopic particles. Specifically, we show that if the density verifies $ \|\rho\|_{L^\infty(0, T; L^\infty)} < \infty $, then the strong solution will exist globally on $ \Bbb R^2\times(0, T) $. Consequently, we generalize the results of Zhong (Discrete Contin. Dyn. Syst. Ser. B, 25 (2020), no. 12, 4603–4615) to the compressible case. In particular, we don't need the additional compatibility condition.

References

[1]	M. Chen, Blowup criterion for viscous, compressible micropolarfluids with vacuum, Nonlinear Anal. Real World Appl., 13 (2012), 850–859. https://doi.org/10.1016/j.nonrwa.2011.08.021 doi: 10.1016/j.nonrwa.2011.08.021
[2]	M. Chen, B. Huang, J. Zhang, Blowup criterion for the three-dimensional equations of compressible viscous micropolar fluids with vacuum, Nonlinear Anal., 79 (2013), 1–11. https://doi.org/10.1016/j.na.2012.10.013 doi: 10.1016/j.na.2012.10.013
[3]	A. C. Eringen, Theory of micropolar fluids, J. Math. Mech. 16 (1966), 1–18. Available from: https://www.jstor.org/stable/24901466
[4]	X. Hou, H. Peng, Global existence for a class large solution to the three-dimensional micropolar fluid equations with vacuum, J. Math. Anal. Appl., 498 (2021), 124931. https://doi.org/10.1016/j.jmaa.2021.124931 doi: 10.1016/j.jmaa.2021.124931
[5]	B. Huang, S. Nečasová, L. Zhang, On the compressible micropolar fluids in a time-dependent domain, Ann. Mat. Pura Appl., 201 (2022), 2733–2795. https://doi.org/10.1007/s10231-022-01218-6 doi: 10.1007/s10231-022-01218-6
[6]	T. Kato, Remarks on the Euler and Navier-Stokes equations in $\Bbb R^2$, Proc. Symp. Pure Math., 45 (1986), 1–7. https://doi.org/10.1090/pspum/045.2/843590 doi: 10.1090/pspum/045.2/843590
[7]	J. Li, Z. Liang, On local classical solutions to the Cauchy problem of the two-dimensional barotropic compressible Navier-Stokes equations with vacuum, J. Math. Pures Appl., 102 (2014) 640–671. https://doi.org/10.1016/j.matpur.2014.02.001
[8]	L. Liu, X. Zhong, Global existence and exponential decay of strong solutions for 2D nonhomogeneous micropolar fluids with density-dependent viscosity, J. Math. Phys., 62 (2021), 061508. https://doi.org/10.1063/5.0055689 doi: 10.1063/5.0055689
[9]	T. Wang, A regularity criterion of strong solutions to the 2D compressible magnetohydrodynamic equations, Nonlinear Anal. Real World Appl., 31 (2016), 100–118. https://doi.org/10.1016/j.nonrwa.2016.01.011 doi: 10.1016/j.nonrwa.2016.01.011
[10]	G. Wu, X. Zhong, Global strong solution and exponential decay of 3D nonhomogeneous asymmetric fluid equations with vacuum, Acta Math. Sci. Ser. B (Engl. Ed.), 41 (2021), 1428–1444. https://doi.org/10.1007/s10473-021-0503-8 doi: 10.1007/s10473-021-0503-8
[11]	X. Zhong, Strong solutions to the Cauchy problem of two-dimensional nonhomogeneous micropolar fluid equations with nonnegative density, Dyn. Partial Differ. Equ., 18 (2021), 49–69. https://dx.doi.org/10.4310/DPDE.2021.v18.n1.a4 doi: 10.4310/DPDE.2021.v18.n1.a4
[12]	X. Zhong, A blow-up criterion of strong solutions to two-dimensional nonhomogeneous micropolar fluid equations with vacuum, Discrete Contin. Dyn. Syst. Ser. B, 25 (2020), 4603–4615. https://doi.org/10.3934/dcdsb.2020115 doi: 10.3934/dcdsb.2020115
[13]	C. Zhu, Q. Tao, Global classical solutions to the compressible micropolar viscous fluids with large oscillations and vacuum, Math. Method. Appl. Sci., 46 (2023), 28–53. https://doi.org/10.1002/mma.8490 doi: 10.1002/mma.8490

Reader Comments

Your name:*

Email:*
© 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)