Local well-posedness of the coupled Yang–Mills and Dirac system for low regularity data

We consider the classical Yang–Mills system coupled with a Dirac equation in 3 + 1 dimensions. Using that most of the nonlinear terms fulfill a null condition we prove local well-posedness for data with minimal regularity assumptions. This problem for smooth data was solved forty years ago by Choquet-Bruhat and Christodoulou. Our result generalises a similar result for the Yang–Mills equation by Selberg and Tesfahun.

Stability and Instability of Traveling Wave Solutions to Nonlinear Wave Equations

In this paper, we study the stability and instability of plane wave solutions to semilinear systems of wave equations satisfying the null condition. We identify a condition that allows us to prove the global nonlinear asymptotic stability of the plane wave. The proof of global stability requires us to analyze the geometry of the interaction between the background plane wave and the perturbation. When this condition is not met, we are able to prove linear instability assuming an additional genericity condition. The linear instability is shown using a geometric optics ansatz.

Absence of WDR13 in p53-Null Mice Increases Longevity

Absence of WDR13 is known to be involved in pancreatic, colon and uterine hyperproliferation. However, a recent study showed its antiproliferative role liver regeneration in response to hepatotoxins. These findings intrigued to study the role of WDR13-null condition in Trp53 knockout mouse to study the tumour predisposition and survival. We report absence of Wdr13 in Trp53-null background alleviates the tumour load, in turn increasing total survival in mouse model.

Local well-posedness of the two-dimensional Dirac–Klein–Gordon equations in Fourier–Lebesgue spaces

The local well-posedness problem is considered for the Dirac–Klein–Gordon system in two space dimensions for data in Fourier–Lebesgue spaces [Formula: see text], where [Formula: see text] and [Formula: see text] and [Formula: see text] denote dual exponents. We lower the regularity assumptions on the data with respect to scaling improving the results of d’Ancona et al. in the classical case [Formula: see text]. Crucial is the fact that the nonlinearities fulfill a null condition as detected by these authors.