Browsing Department of Mathematics by Author "Tesfahun, Achenef"

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Ill-posedness of the Maxwell–Dirac system below charge in space dimension three and lower

Selberg, Sigmund; Tesfahun, Achenef (Journal article; Peer reviewed, 2021)

The Maxwell–Dirac system describes the interaction of an electron with its self-induced electromagnetic field. In space dimension d=3 the system is charge-critical, that is, L2-critical for the spinor with respect to ...
Small data scattering for a cubic Dirac equation with Hartree type nonlinearity in $\R^{1+3}$

Tesfahun, Achenef (Journal article; Peer reviewed, 2020)

We prove that the initial value problem for the Dirac equation $(-i\gamma^\mu \partial_\mu + m) \psi= ( \frac{e^{- |x|}}{|x|} \ast ( \overline \psi \psi)) \psi \quad \text{in } \ \mathbb{R}^{1+3}$ is globally well-posed ...
Well-Posedness for a Dispersive System of the Whitham-Boussinesq Type

Dinvay, Evgueni; Selberg, Sigmund; Tesfahun, Achenef (Journal article; Peer reviewed, 2020)

We regard the Cauchy problem for a particular Whitham--Boussinesq system modeling surface waves of an inviscid incompressible fluid layer. We are interested in well-posedness at a very low level of regularity. We derive ...