A simple but rigorous proof of the Fundamental Theorem of Calculus is given in geometric calculus, after the basis for this theory in geometric algebra has been explained. Various classical examples of this theorem, such as the Green’s and Stokes’ theorem are discussed, as well as the new theory of monogenic functions, which generalizes the concept of an analytic function of a complex variable ...

We prove an L q theory result for generalized Stokes system on a C 2,1 domain complemented with the perfect slip boundary conditions and under Φ−growth conditions. Since the interior regularity was obtained in [3], a regularity up to the boundary is an aim of this paper. In order to get the main result, we use Calderón–Zygmund theory and the method developed in [1]. We obtain higher integrabili...

The nonabelian Stokes theorem, representing a Wilson loop as an integral over all the orien-tations in colour space, and the cumulant expansion are used for derivation of the string effective action in SU(2) gluodynamics. The obtained theory is the theory of the rigid string interacting with the rank two antisymmetric Kalb-Ramond fields. In this model there exists a phase where there are no pro...

Oceanic surface gravity waves have a mean Lagrangian motion, the Stokes drift. The dynamics of winddriven, basin-scale oceanic currents in the presence of Stokes drift are modified by the addition of so-called vortex forces and wave-induced material advection, as well by wave-averaged effects in the surface boundary conditions for the dynamic pressure, sea level, and vertical velocity. Some the...

A Correction to this paper has been published: https://doi.org/10.1007/s00021-020-00502-w

We generalize here the celebrated Partial Regularity Theory of Caffarelli, Kohn and Nirenberg to MHD equations in framework parabolic Morrey spaces. This type generalization using spaces appears be crucial when studying role pressure regularity theory for classical Navier-Stokes as well equations.