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Liu, Yang; Zhou, Nan; Guo, Renying

Global strong solution to the multidimensional inhomogeneous incompressible heat conducting Navier-Stokes flows with vacuum. (English) Zbl 1486.35329

Rocky Mt. J. Math. 51, No. 4, 1315-1328 (2021).
Summary: We are concerned with the Cauchy problem of the multidimensional inhomogeneous incompressible heat conducting Navier-Stokes flows with fractional dissipation. We show that the problem admits a unique global strong solution. Note that the initial data can be arbitrarily large and the initial density can contain vacuum states.

MSC:

35Q30 Navier-Stokes equations
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
80A19 Diffusive and convective heat and mass transfer, heat flow
35D35 Strong solutions to PDEs
35B65 Smoothness and regularity of solutions to PDEs
26A33 Fractional derivatives and integrals
35R11 Fractional partial differential equations

Keywords:

inhomogeneous Navier-Stokes equations; heat conducting flows; global strong solutions; vacuum
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References:

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