This book comprises seven chapters, an appendix, a bibliographical section 98 references,
and an index. Exercises are provided at the end of each chapter. The stated goal of the book …

Since the 1980s, Fourier analysis methods have become of ever greater interest in the study
of linear and nonlinear partial differential equations. In particular, techniques based on …

We develop an efficient dynamically adaptive mesh generator for time-dependent problems
in two or more dimensions. The mesh generator is motivated by the variational approach …

The question of spontaneous apparition of singularity in the 3D incompressible Euler
equations is one of the most important and challenging open problems in mathematical fluid …

For the first time since Lord Kelvin's original conjectures of 1875 we address and study the
time evolution of vortex knots in the context of the Euler equations. The vortex knot is given …

Does three-dimensional incompressible Euler flow with smooth initial conditions develop a
singularity with infinite vorticity after a finite time? This blowup problem is still open. After …

A comparison between vortex stretching (VS) and production of strain/dissipation (PD) is
made with the emphasis on the latter. These two processes are nonlocally interconnected …

We consider the vorticity-stream formulation of axisymmetric incompressible flows and its
equivalence with the primitive formulation. It is shown that, to characterize the regularity of a …

The formation of current sheets in ideal incompressible magnetohydrodynamic flows in two
dimensions is studied numerically using the technique of adaptive mesh refinement. The …

The main purpose of this paper is to bring about a better balance between views of the
exaggerated importance of concentrated vorticity, on one hand, and the underestimated role …