In this paper, we intend to investigate the blow-up problem for the solutions to the partially viscous axisymmetric Hall-MHD equations and local-in-time existence of solutions to such solution with the axisymmetry
. Setting [[omega].sup.[theta]] = [[partial derivative].sub.z][u.sup.r] - [[partial derivative].sub.r][u.sup.z], [OMEGA] = [[omega].sup.[theta]]/r, and [PI] = [B.sup.[theta]]/r, (9) are equivalent to the following equations:
For the case of axisymmetry
, [c.sub.vx] = [c.sub.vy] = [c.sub.vh](say).
"AXIS" indicates axisymmetry
, "HH2" indicates hydraulic modelling with two unknown pressures and two components, and "D" indicates that the points of integration are taken at the tops of the elements.
The "flattened" images are analyzed as having a low surface tension by ADSA, but with continuous cycling the IP film distorted the axisymmetry
of the drop by wrinkling the surface or skewing the drop.
As shown in Figure 1, the assumption of shallow tunnel surrounding rock analytic analysis is as follows: (1) the rock is homogeneous and isotropic; (2) tunnel excavation is a plane strain axisymmetry
problem; (3) the original stress affecting the surrounding rock is not equal in the vertical and the horizontal direction; the static earth pressure coefficient is 0.5.
 reported that significant changes could occur to its natural frequencies and modes when a structure deviates from axisymmetry
because of circumferentially varying model features.
Due to the axisymmetry
, other forces and moments vanish.
The complexity of the problem has forced the usage of sophisticated numerical methods, such as advanced phase field schemes, special nonlinear finite elements, and molecular dynamics simulations [17, 46-50], while analytical derivations have commonly adopted simplifying assumptions, like small deformations, axisymmetry
, and so forth.
An important result based on this axisymmetry
is the well-known steady-state solution for the maximum potential intensity (MPI (2)) that a hurricane can attain under a prescribed thermodynamic condition, which is given by (Emanuel 1986, 2003)