We study Euler solutions via novel function spaces constructed using sparseness and local approximations. In particular, we incorporate Tadmor's scale of regularity spaces (2001) to our framework and applying interpolation/extrapolation methods we give a new approach to convergence of approximate Euler solutions. This is joint work with Mario Milman.
The first-order theories of local fields of positive characteristic, i.e. fields of Laurent series over finite fields, are far less well understood than their characteristic zero analogues: the fields of real, complex and p-adic numbers. On the other hand, the existential theory of an equicharacteristic henselian valued field in the language of valued fields is controlled by the existential theory of its residue field. One is decidable if and only if the other is decidable. When we add a parameter to the language, things get more complicated. Denef and Schoutens […]
