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Recently, many authors studied the regularity problem for the 3D generalized MHD equations (1) intensively.
Maps drawn from such fields are almost surely smooth, so there is no regularity problem ahead.
Such a regularity theory is motivated by one attack on the foliation regularity problem.
By the result of [18], the regularity problem (2.1 - 2.4 2.1 - 2.4 cladmitsl solution ( u ε, v ε ).
Stefanov and Wu [37] proved the global regularity problem on the two-dimensional incompressible Boussinesq equations with fractional dissipation.
This result is applied to an open regularity problem for finite-dimensional realizations of stochastic interest rate models.
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Zheng and Feng [18] very recently gave various estimates of the Green's function of quasilinear subelliptic equations and their applications to regularity problems.
As a preamble, we deal with the Dirichlet and Regularity problems for harmonic functions in convex domains, with optimal nontangential maximal function estimates.
We solve the Neumann, Dirichlet and regularity problems through a new boundary operator method which makes use of operators in the functional calculus of an underlaying first order Dirac type operator.
We prove that Neumann, Dirichlet and regularity problems for divergence form elliptic equations in the half-space are well posed in L2 for small complex L∞ perturbations of a coefficient matrix which is either real symmetric, of block form or constant.
The F-28s had the largest regularity problems, mostly due to the number of landings, which could count up to 16 per day.
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