88 citations · 137 across the 6 of their papers we have counts for
9 papers
Global well-posedness for the massless cubic Dirac equation
Nikolaos Bournaveas, Timothy Candy
We show that the cubic Dirac equation with zero mass is globally well-posed for small data in the scale invariant space H^{\frac{n-1}{2}}(R^n) for n=2, 3. The proof proceeds by usi…
A note on the Chern-Simons-Dirac equations in the Coulomb Gauge
Nikolaos Bournaveas, Timothy Candy, Shuji Machihara
We prove that the Chern-Simons-Dirac equations in the Coulomb gauge are locally well-posed from initial data in H^s with s > 1/4 . To study nonlinear Wave or Dirac equations at thi…
Local and global well-posedness for the Chern-Simons-Dirac system in one dimension
Nikolaos Bournaveas, Timothy Candy, Shuji Machihara
We consider the Cauchy problem for the Chern-Simons-Dirac system on with initial data in . Almost optimal local well-posedness is obtained. Moreover, we sho…
Local well-posedness for the space-time Monopole equation in Lorenz gauge
Nikolaos Bournaveas, Timothy Candy
It is known from the work of Czubak that the space-time Monopole equation is locally well-posed in the Coulomb gauge for small initial data in for . Here…
Mathematical description of bacterial traveling pulses
Nikolaos Bournaveas, Axel Buguin, Vincent Calvez +3
The Keller-Segel system has been widely proposed as a model for bacterial waves driven by chemotactic processes. Current experiments on {\em E. coli} have shown precise structure o…
The one-dimensional Keller-Segel model with fractional diffusion of cells
Nikolaos Bournaveas, Vincent Calvez
We investigate the one-dimensional Keller-Segel model where the diffusion is replaced by a non-local operator, namely the fractional diffusion with exponent . We prove s…