Zero Mach number limit to compressible quantum magnetohydrodynamic equations with vanishing viscosity coefficients

2019 ◽  
Vol 42 (6) ◽  
pp. 1745-1758
Author(s):  
Jianwei Yang ◽  
Fengzhen Que
Keyword(s):  
Mach Number ◽  
Magnetohydrodynamic Equations ◽  
Vanishing Viscosity ◽  
Viscosity Coefficients ◽  
Zero Mach Number Limit

scholarly journals Fujita–Kato solution for compressible Navier–Stokes equations with axisymmetric initial data and zero Mach number limit

2019 ◽  
Vol 22 (05) ◽  
pp. 1950041
Author(s):  
Boris Haspot
Keyword(s):  
Mach Number ◽  
Initial Data ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Small Initial Data ◽  
Dimension Formula ◽  
Global Strong Solution ◽  
Rotational Part ◽  
Zero Mach Number Limit

In this paper, we investigate the question of the existence of global strong solution for the compressible Navier–Stokes equations for small initial data such that the rotational part of the velocity [Formula: see text] belongs to [Formula: see text] (in dimension [Formula: see text]). We show then an equivalent of the so-called Fujita–Kato theorem to the case of the compressible Navier–Stokes equations when we consider axisymmetric initial data. The main difficulty is linked to the fact that in this case the velocity is not Lipschitz, as a consequence we have to study carefully the coupling between the rotational and irrotational part of the velocity. In a second part, we address the question of convergence to the incompressible model (for ill-prepared initial data) when the Mach number goes to zero.

Sign in / Sign up

Export Citation Format

Share Document