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large data existence; suitable weak solution; Navier-Stokes-Fourier equations; incompressible fluid; the viscosity increasing with a scalar quantity; regularity; turbulent kinetic energy model
In this paper, we establish the large-data and long-time existence of a suitable weak solution to an initial and boundary value problem driven by a system of partial differential equations consisting of the Navier-Stokes equations with the viscosity $\nu $ polynomially increasing with a scalar quantity $k$ that evolves according to an evolutionary convection diffusion equation with the right hand side $\nu (k)|{\pmb{\mathsf{D}}}(\vec{v})|^2$ that is merely $L^1$-integrable over space and time. We also formulate a conjecture concerning regularity of such a solution.
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