Existence and uniqueness of solution for a class of non-Newtonian fluids with non-Newtonian potential and damping

Qiu Meng; Yuanyuan Zhao; Wucai Yang; Huifang Xing; Qiu Meng; Yuanyuan Zhao; Wucai Yang; Huifang Xing

doi:10.3934/era.2023148

Electronic Research Archive

2023, Volume 31, Issue 5: 2940-2958. doi: 10.3934/era.2023148

Previous Article Next Article

Research article

Existence and uniqueness of solution for a class of non-Newtonian fluids with non-Newtonian potential and damping

School of Mathematics and Statistics, Beihua University, Jilin 132013, China

Received: 07 February 2023 Revised: 28 February 2023 Accepted: 08 March 2023 Published: 17 March 2023

This paper discusses the existence and uniqueness of local strong solution for a class of 1D non-Newtonian fluids with non-Newtonian potential and damping term. Here we allow the initial vacuum and viscosity term to be fully nonlinear.
- strong solution,
- non-Newtonian fluid,
- vacuum,
- damping,
- non-Newtonian potential
Citation: Qiu Meng, Yuanyuan Zhao, Wucai Yang, Huifang Xing. Existence and uniqueness of solution for a class of non-Newtonian fluids with non-Newtonian potential and damping[J]. Electronic Research Archive, 2023, 31(5): 2940-2958. doi: 10.3934/era.2023148

Related Papers:

Abstract

This paper discusses the existence and uniqueness of local strong solution for a class of 1D non-Newtonian fluids with non-Newtonian potential and damping term. Here we allow the initial vacuum and viscosity term to be fully nonlinear.

References

[1]	O. A. Ladyzhenskaya, New equations for the description of motion of viscous incompressible fluids and solvability in the large of boundary value problems for them, Proc. Steklov Inst. Math., 102 (1967), 95–118.
[2]	L. Yang, K. Du, A comprehensive review on the natural, forced, and mixed convection of non-Newtonian fluids (nanofluids) inside different cavities, J. Therm. Anal. Calorim., 140 (2020), 2033–2054. https://doi.org/10.1007/s10973-019-08987-y doi: 10.1007/s10973-019-08987-y
[3]	Z. P. Xin, S. G. Zhu, Well-posedness of the three-dimensional isentropic compressible Navier-Stokes equations with degenerate viscosities and far field vacuum, J. Math. Pures Appl., 152 (2020), 94–144. https://doi.org/10.1016/j.matpur.2021.05.004 doi: 10.1016/j.matpur.2021.05.004
[4]	W. R. Schowalter, Mechanics of Non-Newtonian Fluids, Pergamon Press, 1978.
[5]	S. Whitaker, Introduction to Fluid Mechanics, Krieger, Melbourne, FL, 1986.
[6]	H. J. Yuan, X. J. Xu, Existence and uniqueness of solutions for a class of non-Newtonian fluids with singularity and vacuum, J. Differ. Equations, 245 (2008), 2871–2916. https://doi.org/10.1016/j.jde.2008.04.013 doi: 10.1016/j.jde.2008.04.013
[7]	T. Kobayashi, T. Suzuki, Weak solutions to the Navier-Stokes-Poisson equation, Adv. Math. Sci. Appl., 18 (2008), 141–168.
[8]	H. Yuan, M. Qiu, Local existence of strong solution for a class of compressible non-Newtonian fluids with non-Newtonian potential, Comput. Math. Appl., 65 (2013), 563–575. https://doi.org/10.1016/j.camwa.2012.10.010 doi: 10.1016/j.camwa.2012.10.010
[9]	Y. Song, H. Yuan, Y. Chen, On the strong solutions of one-dimensional Navier-Stokes-Poisson equations for compressible non-Newtonian fluids, J. Math. Phys., 54 (2013), 229–240. https://doi.org/10.1063/1.4803485 doi: 10.1063/1.4803485
[10]	H. Liu, H. Yuan, J. Qiao, F. Li, Global existence of strong solutions of Navier-Stokes equations with non-Newtonian potential for one-dimensional isentropic compressible fluids, Acta Math. Sci., 32 (2012), 1467–1486. https://doi.org/10.1016/s0252-9602(12)60116-7 doi: 10.1016/s0252-9602(12)60116-7
[11]	H. Li, H. Yuan, Existence and uniqueness of solutions for a class of non-Newtonian fluids with vacuum and damping, J. Math. Anal. Appl., 391 (2012), 223–239. https://doi.org/10.1016/j.jmaa.2012.02.015 doi: 10.1016/j.jmaa.2012.02.015
[12]	C. M. Dafermos, A system of hyperbolic conservation laws with frictional damping, in Theoretical, Experimental, and Numerical Contributions to the Mechanics of Fluids and Solids, Birkhäuser Basel, (1995), 294–307. https://doi.org/10.1007/978-3-0348-9229-2_16
[13]	C. M. Dafermos, R. Pan, Global BV solutions for the P-System with frictional damping, SIAM J. Math. Anal., 41 (2009), 1190–1205. https://doi.org/10.1137/080735126 doi: 10.1137/080735126
[14]	F. Huang, R. Pan, Asymptotic behavior of the solutions to the damped compressible Euler equations with vacuum, J. Differ. Equations, 220 (2006), 207–233. https://doi.org/10.1016/J.JDE.2005.03.012 doi: 10.1016/J.JDE.2005.03.012
[15]	R. Pan, K. Zhao, Initial boundary value problem for compressible Euler equations with damping, Indiana Univ. Math. J., 57 (2008), 2257–2282. https://doi.org/10.1512/iumj.2008.57.3366 doi: 10.1512/iumj.2008.57.3366

Reader Comments

Your name:*

Email:*
© 2023 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)