Local well-posedness of Dirac equations with nonlinearity derived from honeycomb structure in 2 dimensions

DOI10.4134/BKMS.b201040zbMath1490.35371arXiv2106.02843MaRDI QIDQ5033258

Publication date: 22 February 2022

Full work available at URL: https://arxiv.org/abs/2106.02843

Dirac equations local well-posedness non-smoothness honeycomb lattice Bourgain's space

Smoothness and regularity of solutions to PDEs (35B65) Fractional derivatives and integrals (26A33) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Fractional partial differential equations (35R11) Time-dependent Schrödinger equations and Dirac equations (35Q41) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Statistical mechanics of nanostructures and nanoparticles (82D80)

Cites Work

The cubic Dirac equation: small initial data in ${H^{\frac{1}{2}}(\mathbb R^2)}$
Bilinear Fourier restriction estimates related to the 2D wave equation
Sharp well-posedness and ill-posedness results for a quadratic nonlinear Schrödinger equation
Remarks on the semirelativistic Hartree equations
Well-posedness for semi-relativistic Hartree equations of critical type
Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
On the Cauchy problem for the Zakharov system
Higher order fractional Leibniz rule
On the Cauchy problem for the nonlinear semi-relativistic equation in Sobolev spaces
Small data scattering of Dirac equations with Yukawa type potentials in $L_x^2(\mathbb{R}^2)$.
Low regularity well-posedness of Hartree type Dirac equations in 2, 3-dimensions
Small data scattering of 2d Hartree type Dirac equations
On global well-posedness for nonlinear semirelativistic equations in some scaling subcritical and critical cases
Scattering results for Dirac Hartree-type equations with small initial data
The boson star equation with initial data of low regularity
Multilinear weighted convolution of L 2 functions, and applications to nonlinear dispersive equations
Ill-Posedness Issues for the Benjamin--Ono and Related Equations
Analysis of models for quantum transport of electrons in graphene layers
Rigorous derivation of nonlinear Dirac equations for wave propagation in honeycomb structures
Small Data Scattering for Cubic Dirac Equation with Hartree Type Nonlinearity in $\mathbb{R}^{1+3}$
Commutator estimates and the euler and navier-stokes equations
Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
A bilinear estimate with applications to the KdV equation
Long-time Behavior of Solutions to Cubic Dirac Equation with Hartree Type Nonlinearity in ℝ1+2
On the Semirelativistic Hartree‐Type Equation