Serrin-type blowup criterion of three-dimensional nonhomogeneous heat conducting magnetohydrodynamic flows with vacuum

We consider an initial boundary value problem for the nonhomogeneous heat conducting magnetohydrodynamic flows. We show that for the initial density allowing vacuum, the strong solution exists globally if the velocity field satisfies Serrin’s condition. Our method relies upon the delicate energy estimates and regularity properties of Stokes system and elliptic equations

Serrin-type blowup criterion of three-dimensional nonhomogeneous heat conducting magnetohydrodynamic flows with vacuum

We consider an initial boundary value problem for the nonhomogeneous heat conducting magnetohydrodynamic flows. We show that for the initial density allowing vacuum, the strong solution exists globally if the velocity field satisfies Serrin’s condition. Our method relies upon the delicate energy estimates and regularity properties of Stokes system and elliptic equations

Global strong solutions of the density-dependent incompressible MHD system with zero resistivity in a bounded domain

In this paper, we first establish a regularity criterion for the strong solutions to the density-dependent incompressible MHD system with zero resistivity in a bounded domain. Then we use it and the bootstrap argument to prove the global well-posedness provided that the initial data u0 and b0 satisfy that (d-2)||∇u0 || L2+||b0||w1,p are sufficiently small with . We do not assume the positivity of initial density, it may vanish in an open subset (vacuum) of Ω

Sub-grid effects of the Voigt viscoelastic regularization of a singular dyadic model of turbulence

In this work we investigate the spectral signature of Navier–Stokes–Voigt (NSV) viscoelastic fluid flows by employing numerical simulations of a singular dyadic shell model. Our results clearly show that as the relaxation time is increased above a threshold, the inertial range is reduced, conserving part of the large-scale statistics. These results differ drastically from the two power-law scenarios observed in a previous work, where the NSV model was studied via Sabra shell model simulations instead. We also show that the additional elastic term regularizes the singular dyadic model, which is the main reason behind this reduction of degrees of freedom. The results of this work aim at proposing the NSV regularization as a sub-grid model.Indisponível

Local well-posedness and low Mach number limit of the compressible magnetohydrodynamic equations in critical spaces

The local well-posedness and low Mach number limit are considered for the multi-dimensional isentropic compressible viscous magnetohydrodynamic equations in critical spaces. First the local well-posedness of solution to the viscous magnetohydrodynamic equations with large initial data is established. Then the low Mach number limit is studied for general large data and it is proved that the solution of the compressible magnetohydrodynamic equations converges to that of the incompressible magnetohydrodynamic equations as the Mach number tends to zero. Moreover, the convergence rates are obtained.Comment: 37page