We prove that if u(t) is a log-log blow-up solution, of the type studied by Merle-Raphaël [14], to the L critical focusing NLS equation i∂tu+∆u+|u|u = 0 with initial data u0 ∈ H(R) in the cases d = 1, 2, then u(t) remains bounded in H away from the blow-up point. This is obtained without assuming that the initial data u0 has any regularity beyond H(R). As an application of the d = 1 result, we ...

In Part I of this series [A. Poveda, A. Rinot and D. Sinapova, Sigma-Prikry forcing I: The axioms, Canad. J. Math. 73(5) (2021) 1205–1238], we introduced a class notions which call [Formula: see text]-Prikry, showed that many the known Prikry-type center around singular cardinals countable cofinality are text]-Prikry. We given text]-Prikry poset text] text]-name for non-reflecting stationary se...

In this paper, we consider a semilinear parabolic equation ut = ∆u + u q ∫ t 0 u(x, s)ds, x ∈ Ω, t > 0 with nonlocal nonlinear boundary condition u|∂Ω×(0,+∞) = ∫ Ω φ(x, y)u (y, t)dy and nonnegative initial data, where p, q ≥ 0 and l > 0. The blow-up criteria and the blow-up rate are obtained.

We consider the classical problem of the blowing-up of solutions of the nonlinear heat equation. We show that there exist infinitely many profiles around the blow-up point, and for each integer k, we construct a set of codimension 2k in the space of initial data giving rise to solutions that blow-up according to the given profile.

Model equations are derived from what we call the strain-vorticity dynamics of the incompressible viscous uid motion. The global existence and blow-up are examined for them and we see that the L 1 norm of the vorticity plays an important role. Blow-up solutions are obtained as self-similar solutions.

An isolated massive star can blow a bubble, while a group of massive stars can blow superbubbles. In this paper, we examine three intriguing questions regarding bubbles and superbubbles: (1) why don’t we see interstellar bubbles around every O star? (2) how hot are the bubble interiors? and (3) what is going on at the hot/cold gas interface in a bubble?

We present here the draft genome sequence of a Providencia stuartii strain, derived from the salivary glands of larval Lucilia sericata, a common blow fly important to forensic, medical, and veterinary science. The genome sequence will help dissect coinfections involving P. stuartii and Proteus mirabilis, as well as blow fly-bacteria interactions.