Abstract
In this note, we study the blowup of classical solutions to the three-dimensional compressible Navier–Stokes equations with revised Maxwell’s law. First, we improve the previous blowup result with initial density away from vacuum by removing three restrictions. Next, we present a blowup result for the classical solutions with decay at far fields when the shear relaxation time is zero by introducing a new averaged quantity.
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References
Bian, D.F., Li, J.K.: Finite time blow up of compressible Navier–Stokes equations on half space or outside a fixed ball. J. Differ. Equ. 267(12), 7047–7063 (2019)
Chakraborty, D., Sader, J.E.: Constitutive models for linear compressible viscoelastic flows of simple liquids at nanometer length scales. Phys. Fluids 27, 052002-1–052002-13 (2015)
Cho, Y., **, B.: Blow up of viscous heat-conducting compressible flows. J. Math. Anal. Appl. 320, 819–826 (2006)
Hu, Y.X., Racke, R.: Compressible Navier–Stokes equations with revised Maxwells law. J. Math. Fluid Mech. 19, 77–90 (2017)
Jiu, Q.S., Wang, Y.X., **n, Z.P.: Remarks on blow-up of smooth solutions to the compressible fluid with constant and degenerate viscosities. J. Differ. Equ. 259, 2981–3003 (2015)
Li, M.L., Yao, Z.A., Yu, R.F.: Non-existence of global classical solutions to barotropic compressible Navier–Stokes equations with degenerate viscosity and vacuum. J. Differ. Equ. 306(5), 280–295 (2022)
Rozanova, O.: Blow-up of smooth highly decreasing at infinity solutions to the compressible Navier–Stokes equations. J. Differ. Equ. 245, 1762–1774 (2008)
Sideris, T.C.: Formation of singularities in three-dimensional compressible fluids. Commun. Math. Phys. 101, 475–485 (1985)
Wang, G.W., Guo, B.L., Fang, S.M.: Blow-up of the smooth solutions to the compressible Navier–Stokes equations. Math. Methods Appl. Sci. 40, 5262–5272 (2017)
Wang, N., Hu, Y.X.: Blowup of solutions for compressible Navier–Stokes equations with revised Maxwells law. Appl. Math. Lett. 103, 106221 (2020)
Wang, Z., Hu, Y.X.: Low Mach number limit of full compressible Navier–Stokes equations with revised Maxwell law. J. Math. Fluid Mech. 24, 6 (2022)
**n, Z.P.: Blowup of smooth solutions to the compressible Navier–Stokes equations with compact density. Commun. Pure Appl. Math. 51, 229–240 (1998)
**n, Z.P., Yan, W.: On blow up of classical solutions to the compressible Navier–Stokes equations. Commun. Math. Phys. 321, 529–541 (2013)
Yong, W.A.: Newtonian limit of Maxwell fluid flows. Arch. Ration. Mech. Anal. 214, 913–922 (2014)
Acknowledgements
This work is supported by the Project of Youth Backbone Teachers of Colleges and Universities in Henan Province (2019GGJS176) and the Vital Science Research Foundation of Henan Province Education Department (22A110024).
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Communicated by Yong Zhou.
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Dong, J. Remarks on Blowup of Solutions for Compressible Navier–Stokes Equations with Revised Maxwell’s Law. Bull. Malays. Math. Sci. Soc. 46, 38 (2023). https://doi.org/10.1007/s40840-022-01437-3
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DOI: https://doi.org/10.1007/s40840-022-01437-3