Close Search Advanced
Journals
Resources
About Us
Open Access

Global Existence of Large Data Weak Solutions for a Simplified Compressible Oldroyd-B Model Without Stress Diffusion

Global Existence of Large Data Weak Solutions for a Simplified Compressible Oldroyd-B Model Without Stress Diffusion
Read Now
Download (PDF)

Year:    2020

Author:    Yong Lu, Milan Pokorný

Analysis in Theory and Applications, Vol. 36 (2020), Iss. 3 : pp. 348–372

Abstract

We start with the compressible Oldroyd-B model derived in [2] (J. W. Barrett, Y. Lu, and E. Süli,  Existence of large-data finite-energy global weak solutions to a compressible Oldroyd-B model, Commun. Math. Sci., 15 (2017), 1265-1323), where the existence of global-in-time finite-energy weak solutions was shown in two dimensional setting with stress diffusion. In the paper, we investigate the case without stress diffusion. We first restrict ourselves to the corotational setting as in [28] (P. L. Lions, and N. Masmoudi, Global solutions for some Oldroyd models of non-Newtonian flows, Chin. Ann. Math., Ser. B, 21(2) (2000), 131-146). We further assume the extra stress tensor is a scalar matrix and we derive a simplified model which takes a similar form as the multi-component compressible Navier-Stokes equations, where, however, the pressure term related to the scalar extra stress tensor has the opposite sign. By employing the techniques developed in [30,35], we can still prove the global-in-time existence of finite energy weak solutions in two or three dimensions, without the presence of stress diffusion.

Submit Article

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.OA-SU3

Analysis in Theory and Applications, Vol. 36 (2020), Iss. 3 : pp. 348–372

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords:    Compressible Oldroyd-B model stress diffusion weak solutions negative pressure term.

Author Details

Yong Lu

Milan Pokorný

  1. The Cauchy problem for an inviscid Oldroyd-B model in three dimensions: global well posedness and optimal decay rates

    Liu, Sili | Wang, Wenjun | Wen, Huanyao

    Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 153 (2023), Iss. 2 P.441

    https://doi.org/10.1017/prm.2022.2 [Citations: 2]

  2. Global Well-Posedness and Optimal Time Decay Rates for the Generalized Phan-Thien-Tanner Model in ℝ3

    Chen, Yuhui | Yao, Qinghe | Li, Minling | Yao, Zheng-an

    Acta Mathematica Scientia, Vol. 43 (2023), Iss. 3 P.1301

    https://doi.org/10.1007/s10473-023-0317-y [Citations: 0]

  3. Global wellposedness and large time behavior of solutions to the N-dimensional compressible Oldroyd-B model

    Zhai, Xiaoping | Li, Yongsheng

    Journal of Differential Equations, Vol. 290 (2021), Iss. P.116

    https://doi.org/10.1016/j.jde.2021.04.027 [Citations: 12]

  4. The sharp time decay rates for the incompressible Phan-Thien–Tanner system with magnetic field in R2

    Chen, Yuhui | Li, Minling | Yao, Qinghe | Yao, Zheng-an

    Applied Mathematics Letters, Vol. 129 (2022), Iss. P.107965

    https://doi.org/10.1016/j.aml.2022.107965 [Citations: 0]

  5. Global solutions to the three-dimensional inhomogeneous incompressible Phan-Thien–Tanner system with a class of large initial data

    Chen, Yuhui | Li, Minling | Yao, Qinghe | Yao, Zheng-an

    Nonlinearity, Vol. 37 (2024), Iss. 9 P.095035

    https://doi.org/10.1088/1361-6544/ad6b6f [Citations: 0]

  6. The sharp time decay rates and stability of large solutions to the two-dimensional Phan-Thien–Tanner system with magnetic field

    Chen, Yuhui | Li, Minling | Yao, Qinghe | Yao, Zheng-an

    Asymptotic Analysis, Vol. 129 (2022), Iss. 3-4 P.451

    https://doi.org/10.3233/ASY-211736 [Citations: 1]

  7. Sharp Rates of Decay and Global-in-Time Stability of Large Solutions to The Three-Dimensional Incompressible Phan-Thien–Tanner System of Polymeric Flows

    Chen, Yuhui | Li, Minling | Yao, Qinghe | Yao, Zheng-an

    SIAM Journal on Mathematical Analysis, Vol. 55 (2023), Iss. 5 P.4537

    https://doi.org/10.1137/21M1435161 [Citations: 4]

  8. Remarks on global weak solutions to a two-fluid type model

    Wen, Huanyao | Zhu, Changjiang

    Communications on Pure & Applied Analysis, Vol. 20 (2021), Iss. 7-8 P.2839

    https://doi.org/10.3934/cpaa.2021072 [Citations: 4]

  9. The optimal time decay rates for the compressible Oldroyd-B model in ℝ 3

    Chen, Yuhui | Li, Minling | Yao, Qinghe | Yao, Zheng-an

    Applicable Analysis, Vol. 103 (2024), Iss. 2 P.519

    https://doi.org/10.1080/00036811.2023.2197452 [Citations: 0]

  10. Coupling the Navier–Stokes–Fourier equations with the Johnson–Segalman stress-diffusive viscoelastic model: Global-in-time and large-data analysis

    Bathory, Michal | Bulíček, Miroslav | Málek, Josef

    Mathematical Models and Methods in Applied Sciences, Vol. 34 (2024), Iss. 03 P.417

    https://doi.org/10.1142/S0218202524500064 [Citations: 1]

  11. On the Cauchy Problem for a Compressible Oldroyd-B Model Without Stress Diffusion

    Liu, Sili | Lu, Yong | Wen, Huanyao

    SIAM Journal on Mathematical Analysis, Vol. 53 (2021), Iss. 6 P.6216

    https://doi.org/10.1137/20M1362243 [Citations: 5]