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Global strong solutions for 3D viscous incompressible heat conducting Navier‐Stokes flows with the general external force
Author(s) -
Wang Wan,
Yu Haibo,
Zhang Peixin
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4915
Subject(s) - mathematics , compressibility , boundary value problem , navier–stokes equations , mechanics , classical mechanics , mathematical analysis , physics
In this paper, we consider the initial boundary value problem for the nonhomogeneous heat–conducting fluids with non‐negative density and the general external force. We prove that there exists a unique global strong solution to the 3D viscous nonhomogeneous heat–conducting Navier‐Stokes flows if μ − 4ρ ¯ 3 ( ‖ ρ u 0‖L 22 + ‖ f ‖L t 2L x 2) ( ‖ ∇ u 0‖L 22 + 5 2μ − 1ρ ¯ ‖ f ‖L t 2L x 2) is suitably small.