Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Blow-up criteria of smooth solutions for the 3D micropolar fluid equations are investigated. Logarithmically improved blow-up criteria are established in the Morrey-Campanto space.

We prove here the existence of boundary blow up solutions for fully nonlinear equations in general domains, for a nonlinearity satisfying KellerOsserman type condition. If moreover the nonlinearity is non decreasing , we prove uniqueness for boundary blow up solutions on balls for operators related to Pucci’s operators.

In this paper, we give a symplectic proof for Seiberg-Witten blow-up formula of four dimensional symplectic manifolds, especially we interpret a strange phenomenon that the genera of embedding J-holomorphic curves will decrease when we symplectically blow-up the four dimensional symplectic manifold.

We use the bifurcation method of dynamical systems to study the periodic wave solutions and their limits for the generalized KP-BBM equation. A number of explicit periodic wave solutions are obtained. These solutions contain smooth periodic wave solutions and periodic blow-up solutions. Their limits contain periodic wave solutions, kink wave solutions, unbounded wave solutions, blow-up wave sol...

We evaluated the acute toxicities and the physiological effects of plant monoterpenoids (eugenol, pulegone, citronellal and alpha-terpineol) and neuroactive insecticides (malathion, dieldrin and RH3421) on flight muscle impulses (FMI) and wing beat signals (WBS) of the blow fly (Phaenicia sericata). Topically-applied eugenol, pulegone, citronellal, and alpha-terpineol produced neurotoxic sympto...

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 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?