On axially symmetric incompressible magnetohydrodynamics in three dimensions
By Zhen Lei. 2012
177 citations recorded by the source corpus.
Abstract In the short article we study the ideal incompressible magnetohydrodynamic equations in three dimensions in which the Faraday law is inviscid. We prove the global well-posedness of classical solutions for a family of special axisymmetric initial data whose swirl components of the velocity field and magnetic vorticity field are trivial.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/360ae653741b27fccf4619bcd52604c794a3a970
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In Applied Mathematics
In Mathematical Physics
Citations in the corpus
- Global Well-Posedness of the Incompressible Magnetohydrodynamics (2016, background): “Lei was the first to construct a family of solutions without any smallness constraints in the presence of axis symmetry [12] in three dimensions.”
- Liouville type theorems for the steady axially symmetric Navier-Stokes and magnetohydrodynamic equations (2015, unknown): “R3) ≤ 2 2/3C ∗ ∇ u r r 2/3 L2(R3) kΛkL2(R3). (2.27) We still need to explore the relation between ur r and Ωby introducing the stream function, this relation was already known in the unsteady case [5, 16]. By the divergence free condition, ∂r(rur)+∂z(ruz) = 0, one can introduce a stream function ψθ”
- Singularity formation for the incompressible Hall-MHD equations without resistivity (2013, result): “1.5) Ω(t= 0,r,z) = Ω0(r,z) := ω0θ(r,z) r , (1.6) Π(t= 0,r,z) = Π0(r,z) := b0θ(r,z) r . (1.7) We refer two closely related results on the axisymmetric solution to the usual MHD or Hall-MHD system. Lei [16] has showed that the existence ofglobal in time smooth solution to the incompressible viscous MH”