Remarks on blowup of solutions for one‐dimensional compressible Navier–Stokes equations with Maxwell's law

Jianwei Dong, Qiao Zhang and Yong Yang

Mathematische Nachrichten, 2023, vol. 296, issue 10, 4523-4532

Abstract: In this note, we present some blowup results of solutions to the one‐dimensional compressible Navier–Stokes equations with Maxwell's law. First, we improve the blowup result of Hu and Wang [Math. Nachr. 92 (2019), 826–840] with initial density away from vacuum by removing two restrictions. Next, we give a blowup result for the solutions with decay at far fields. Finally, we construct some special analytical solutions to exhibit the blowup or non‐blowup phenomena for the relaxed system.

Date: 2023
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https://doi.org/10.1002/mana.202200260

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