Regularity Criteria of the Three-dimensional Mhd System Involving One Velocity and One Vorticity Component
نویسنده
چکیده
We obtain a regularity criteria of the solution to the three-dimensional magnetohydrodynamics system to remain smooth for all time involving only one velocity and one vorticity component. Moreover, the norm in space and time with which we impose our criteria for the vorticity component is at the scaling invariant level. The proof requires a new decomposition of the four nonlinear terms making use of a new identity due to the divergence-free conditions of the velocity and the magnetic vector fields.
منابع مشابه
Remarks on the regularity criteria of three-dimensional magnetohydrodynamics system in terms of two velocity field components
Articles you may be interested in Remarks on the regularity criteria of generalized MHD and Navier-Stokes systems Regularity criteria of weak solutions to the three-dimensional micropolar flows Remarks on the blow-up criteria for three-dimensional ideal magnetohydrodynamics equations We study the three-dimensional magnetohydrodynamics system and obtain its regularity criteria in terms of only t...
متن کاملRegularity of a Weak Solution to the Navier-Stokes Equations via One Component of a Spectral Projection of Vorticity
The lecture is motivated by the regularity criteria, showing that some particular quantities (one or two components of velocity, two components of vorticity, some chosen components of the gradient of velocity, etc) control the regularity of a weak solution to the Navier–Stokes equations. We show that a certain spectral projection of vorticity, or even one its component, also belong to such quan...
متن کاملOn the regularity of the axisymmetric solutions of the Navier-Stokes equations
Weobtain improved regularity criteria for the axisymmetricweak solutions of the three dimensional Navier-Stokes equations with nonzero swirl. In particular we prove that the integrability of single component of vorticity or velocity fields, in terms of norms with zero scaling dimension give sufficient conditions for the regularity of weak solutions. To obtain these criteria we derive new a prio...
متن کاملTwo regularity criteria for the 3D MHD equations
This work establishes two regularity criteria for the 3D incompressible MHD equations. The first one is in terms of the derivative of the velocity field in one-direction while the second one requires suitable boundedness of the derivative of the pressure in one-direction.
متن کاملMHD Three-Dimensional Stagnation-Point Flow and Heat Transfer of a Nanofluid over a Stretching Sheet
In this study, the three-dimensional magnetohydrodynamic (MHD) boundary layer of stagnation-point flow in a nanofluid was investigated. The Navier–Stokes equations were reduced to a set of nonlinear ordinary differential equations using a similarity transform. The similarity equations were solved for three types of nanoparticles: copper, alumina and titania with water as the base fluid, to inve...
متن کامل