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EXISTENCE OF WEAK SOLUTIONS TO p-NAVIER-STOKES EQUATIONS

Publication ,  Journal Article
Feng, Y; Li, L; Liu, JG; Xu, X
Published in: Discrete and Continuous Dynamical Systems Series B
April 1, 2024
Published version (DOI)

We study the existence of weak solutions to the p-Navier-Stokes equations with a symmetric p-Laplacian on bounded domains. We construct a particular Schauder basis in W01, p(Ω) with divergence free constraint and prove existence of weak solutions using the Galerkin approximation via this basis. Meanwhile, in the proof, we establish a chain rule for the Lp integral of the weak solutions, which fixes a gap in our previous work. The equality of energy dissipation is also established for the weak solutions considered.

Duke Scholars

Xiaoqian Xu
Author Xiaoqian Xu DKU Faculty
Jian-Guo Liu
Author Jian-Guo Liu Physics

Published In

Discrete and Continuous Dynamical Systems Series B

DOI

10.3934/dcdsb.2023159

ISSN

1531-3492

Publication Date

April 1, 2024

Volume

29

Issue

4

Start / End Page

1868 / 1890

Related Subject Headings

  • Applied Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

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ICMJE
MLA
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Feng, Y., Li, L., Liu, J. G., & Xu, X. (2024). EXISTENCE OF WEAK SOLUTIONS TO p-NAVIER-STOKES EQUATIONS. Discrete and Continuous Dynamical Systems Series B, 29(4), 1868–1890. https://doi.org/10.3934/dcdsb.2023159
Feng, Y., L. Li, J. G. Liu, and X. Xu. “EXISTENCE OF WEAK SOLUTIONS TO p-NAVIER-STOKES EQUATIONS.” Discrete and Continuous Dynamical Systems Series B 29, no. 4 (April 1, 2024): 1868–90. https://doi.org/10.3934/dcdsb.2023159.
Feng Y, Li L, Liu JG, Xu X. EXISTENCE OF WEAK SOLUTIONS TO p-NAVIER-STOKES EQUATIONS. Discrete and Continuous Dynamical Systems Series B. 2024 Apr 1;29(4):1868–90.
Feng, Y., et al. “EXISTENCE OF WEAK SOLUTIONS TO p-NAVIER-STOKES EQUATIONS.” Discrete and Continuous Dynamical Systems Series B, vol. 29, no. 4, Apr. 2024, pp. 1868–90. Scopus, doi:10.3934/dcdsb.2023159.
Feng Y, Li L, Liu JG, Xu X. EXISTENCE OF WEAK SOLUTIONS TO p-NAVIER-STOKES EQUATIONS. Discrete and Continuous Dynamical Systems Series B. 2024 Apr 1;29(4):1868–1890.

Published In

Discrete and Continuous Dynamical Systems Series B

DOI

10.3934/dcdsb.2023159

ISSN

1531-3492

Publication Date

April 1, 2024

Volume

29

Issue

4

Start / End Page

1868 / 1890

Related Subject Headings

  • Applied Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics