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Bounds on the growth of high Sobolev norms of solutions to the fractional nonlinear Schrödinger equation on and
Antonios Kapetanios, José L. Rodrigo, Vedran Sohinger
We prove polynomial bounds on the growth of high Sobolev norms of solutions to the defocusing fractional nonlinear Schrödinger equation with cubic and Hartree-type nonlinearities i…
On 2D Harmonic Extensions of Vector Fields and Stellarator Coils
Adam J. Golab, James C. Robinson, José L. Rodrigo
We consider a problem relating to magnetic confinement devices known as stellarators. Plasma is confined by magnetic fields generated by current-carrying coils, and here we investi…
Remarks on a nonlocal transport
Dong Li, Jose Rodrigo
We consider a one dimensional nonlocal transport equation and its natural multi-dimensional analogues. By using a new pointwise inequality for the Hilbert transform, we give a shor…
Local Existence of Analytic Sharp Fronts for Singular SQG
Calvin Khor, José L. Rodrigo
In this paper, we prove local existence and uniqueness of analytic sharp-front solutions to a generalised SQG equation by the use of an abstract Cauchy--Kowalevskaya theorem. Here,…
On Sharp Fronts and Almost-Sharp Fronts for singular SQG
Calvin Khor, José L. Rodrigo
In this paper we consider a family of active scalars with a velocity field given by , for . This family of equations is a more singular ve…
Asymptotics for vortex filaments using a modified Biot-Savart kernel
Benjamin C. Pooley, José L. Rodrigo
We consider a family of approximations to the Euler equations obtained by adding to the non-locality in the Biot-Savart kernel together with a mollification (with par…