EXISTENCE OF WEAK SOLUTIONS TO p-NAVIER-STOKES EQUATIONS

Authors

Feng, Y; Li, L; Liu, JG; Xu, X

Abstract

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.

Citation

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.
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