Existence of regular time-periodic solutions for a class of non-Newtonian double-diffusive convection system

Qiong Wu; Changjia Wang

Applications of Mathematics (2025)

  • Issue: 3, page 387-411
  • ISSN: 0862-7940

Abstract

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We investigate a system of partial differential equations that models the motion of an incompressible double-diffusion convection fluid. The additional stress tensor is generated by a potential with p -structure. In a three-dimensional periodic setting and p ∈ [ 5 3 , 2 ) , we employ a regularized approximation scheme in conjunction with the Galerkin method to establish the existence of regular solutions, provided that the forcing term is properly small. Furthermore, we demonstrate the existence of periodic regular solutions with period T when the external force exhibits periodicity in time with the same period T .

How to cite

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Wu, Qiong, and Wang, Changjia. "Existence of regular time-periodic solutions for a class of non-Newtonian double-diffusive convection system." Applications of Mathematics (2025): 387-411. <http://eudml.org/doc/299994>.

@article{Wu2025,
abstract = {We investigate a system of partial differential equations that models the motion of an incompressible double-diffusion convection fluid. The additional stress tensor is generated by a potential with $p$-structure. In a three-dimensional periodic setting and $p\in [\frac\{5\}\{3\},2)$, we employ a regularized approximation scheme in conjunction with the Galerkin method to establish the existence of regular solutions, provided that the forcing term is properly small. Furthermore, we demonstrate the existence of periodic regular solutions with period $T$ when the external force exhibits periodicity in time with the same period $T$.},
author = {Wu, Qiong, Wang, Changjia},
journal = {Applications of Mathematics},
keywords = {double-diffusive convection fluid; non-Newtonian; periodic regular solution},
language = {eng},
number = {3},
pages = {387-411},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence of regular time-periodic solutions for a class of non-Newtonian double-diffusive convection system},
url = {http://eudml.org/doc/299994},
year = {2025},
}

TY - JOUR
AU - Wu, Qiong
AU - Wang, Changjia
TI - Existence of regular time-periodic solutions for a class of non-Newtonian double-diffusive convection system
JO - Applications of Mathematics
PY - 2025
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 3
SP - 387
EP - 411
AB - We investigate a system of partial differential equations that models the motion of an incompressible double-diffusion convection fluid. The additional stress tensor is generated by a potential with $p$-structure. In a three-dimensional periodic setting and $p\in [\frac{5}{3},2)$, we employ a regularized approximation scheme in conjunction with the Galerkin method to establish the existence of regular solutions, provided that the forcing term is properly small. Furthermore, we demonstrate the existence of periodic regular solutions with period $T$ when the external force exhibits periodicity in time with the same period $T$.
LA - eng
KW - double-diffusive convection fluid; non-Newtonian; periodic regular solution
UR - http://eudml.org/doc/299994
ER -

References

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  1. Abbatiello, A., Maremonti, P., 10.1007/s00021-019-0435-4, J. Math. Fluid Mech. 21 (2019), Article ID 29, 14 pages. (2019) Zbl1416.35177MR3938375DOI10.1007/s00021-019-0435-4
  2. Adams, R. A., Fournier, J. J. F., 10.1016/s0079-8169(03)x8001-0, Pure and Applied Mathematics 140. Academic Press, Amsterdam (2003). (2003) Zbl1098.46001MR2424078DOI10.1016/s0079-8169(03)x8001-0
  3. Astarita, G., Marrucci, G., Principles of Non-Newtonian Fluid Mechanics, McGraw-Hill, London (1974). (1974) 
  4. Belov, V. Y., Kapitonov, B. V., 10.1007/bf00970307, Sib. Math. J. 24 (1983), 823-833. (1983) Zbl0599.35129MR0731038DOI10.1007/bf00970307
  5. Chen, F., Guo, B., 10.1080/00036811.2018.1441995, Appl. Anal. 98 (2019), 1724-1740. (2019) Zbl1417.35114MR3955790DOI10.1080/00036811.2018.1441995
  6. Chen, F., Guo, B., Zeng, L., 10.1002/mma.4895, Math. Methods Appl. Sci. 41 (2018), 4327-4336. (2018) Zbl1397.35201MR3824560DOI10.1002/mma.4895
  7. Chen, F., Guo, B., Zeng, L., 10.1063/1.5052668, J. Math. Phys. 60 (2019), Article ID 011511, 14 pages. (2019) Zbl1406.76078MR3903541DOI10.1063/1.5052668
  8. Diening, L., Ebmeyer, C., Růžička, M., 10.1137/05064120x, SIAM J. Numer. Anal. 45 (2007), 457-472. (2007) Zbl1140.65060MR2300281DOI10.1137/05064120x
  9. Joseph, D. D., 10.1007/978-3-642-80991-0, Springer Tracts in Natural Philosophy 27. Springer, Berlin (1976). (1976) Zbl0345.76022MR0449147DOI10.1007/978-3-642-80991-0
  10. Lorca, S. A., Rojas-Medar, M. A., Weak solutions for the viscous incompressible chemically active fluids, Rev. Mat. Estat. 14 (1996), 183-199. (1996) Zbl0894.76091MR1465922
  11. Málek, J., Rajagopal, K. R., 10.1016/s1874-5717(06)80008-3, Evolutionary Equations II Handbook of Differential Equations. Elsevier/North-Holland, Amsterdam (2005), 371-459. (2005) Zbl1095.35027MR2182831DOI10.1016/s1874-5717(06)80008-3
  12. Moretti, A. C., Rojas-Medar, M. A., Rojas-Medarm, M. D., 10.1016/s0898-1221(02)00148-7, Comput. Math. Appl. 44 (2002), 287-299. (2002) Zbl1179.76015MR1912828DOI10.1016/s0898-1221(02)00148-7
  13. Nečas, J., Málek, J., Rokyta, M., Růžička, M., 10.1007/978-1-4899-6824-1, Applied Mathematics and Mathematical Computation 13. Chapman & Hall, London (1996). (1996) Zbl0851.35002MR1409366DOI10.1007/978-1-4899-6824-1
  14. Pedlosky, J., 10.1007/978-1-4684-0071-7, Springer, New York (1979). (1979) Zbl0429.76001DOI10.1007/978-1-4684-0071-7
  15. Radko, T., 10.1017/cbo9781139034173, Cambridge University Press, Cambridge (2013). (2013) Zbl1301.76001MR3183649DOI10.1017/cbo9781139034173
  16. Ragusa, M. A., Wu, F., 10.57262/ade026-0708-281, Adv. Differ. Equ. 26 (2021), 281-304. (2021) Zbl1479.35694MR4305007DOI10.57262/ade026-0708-281
  17. Rojas-Medar, M. A., Lorca, S. A., Global strong solution of the equations for the motion of a chemical active fluid, Mat. Contemp. 8 (1995), 319-335. (1995) Zbl0853.35096MR1330043
  18. Rojas-Medar, M. A., Lorca, S. A., The equations of a viscous incompressible chemical active fluid I: Uniqueness and existence of the local solutions, Rev. Mat. Apl. 16 (1995), 57-80. (1995) Zbl0849.35101MR1382269
  19. Rojas-Medar, M. A., Lorca, S. A., The equations of a viscous incompressible chemical active fluid II: Regularity of solutions, Rev. Mat. Apl. 16 (1995), 81-95. (1995) Zbl1126.35350MR1382270
  20. Wu, F., 10.1007/s40840-019-00828-3, Bull. Malays. Math. Sci. Soc. (2) 43 (2020), 2673-2686. (2020) Zbl1443.76208MR4089665DOI10.1007/s40840-019-00828-3
  21. Wu, F., 10.1007/s00021-020-0483-9, J. Math. Fluid Mech. 22 (2020), Article ID 24, 9 pages. (2020) Zbl1435.35313MR4085356DOI10.1007/s00021-020-0483-9
  22. Wu, F., 10.1080/00036811.2023.2260419, Appl. Anal. 103 (2024), 1693-1703. (2024) Zbl1545.35127MR4754792DOI10.1080/00036811.2023.2260419

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