I am pleased to announce the release of my new preprint:
Gauge Transforms and Strichartz Estimates for Benjamin–Ono-Type Dirac Equations
This work studies a Benjamin–Ono-type Dirac equation on R^n , involving the Dirac operator associated with the Clifford algebra of signature (0,n), the fractional Riesz operator, and a scalar-valued quadratic nonlinearity.
Under a pointwise anticommutation condition and a uniform dyadic regularity assumption on the spatial Fourier profile of the solution, a unit-modulus gauge transform is constructed. The associated Plemelj components reduce the original equation to a coupled Schrödinger system with gauge nonlinearities.
The paper establishes:
- a priori estimates for homogeneous Sobolev seminorms;
- bounds for the resulting gauge nonlinearities;
- Strichartz-type estimates for sharp Schrödinger-admissible pairs;
- at most exponential growth of the relevant Sobolev controls on finite time intervals.
The results apply in dimensions n>=3 and connect gauge transforms, Clifford analysis, fractional Dirac operators, harmonic analysis, and dispersive estimates.
The preprint is available on arXiv:
Comments and suggestions are very welcome.
