We show that the particle motion in Bohmian mechanics, given by the solution of an ordinary differential equation, exists globally: For a large class of potentials the singularities of the velocity field and infinity will not be reached in finite time for typical initial values. A substantial part of the analysis is based on the probabilistic significance of the quantum flux. We elucidate the c...

We survey some known facts and open questions concerning the global properties of 3+1 dimensional space–times containing a compact Cauchy surface. We consider space–times with an l–dimensional Lie algebra of space–like Killing fields. For each l ≤ 3, we give some basic results and conjectures on global existence and cosmic censorship. For the case of the 3+1 dimensional Einstein equations witho...

Let be a semiiow on a complete metric space W. Assume that is-contracting (in the sense of Kuratowski) and point dissipative. We show here that has a global attractor in W. This is an improvement over earlier results in which a further assumption, wherein the orbit of each bounded set is bounded, is made for. Furthermore, this result includes the Billotti-LaSalle Theorem, where is assumed to be...

In this paper, we consider complex Ginzburg-Landau equations of the form u t ? u + P(juj 2)u = 0 in R N where P is a polynomial of degree K with complex coeecients and is a complex number with positive real part <. If the real part of the highest coeecient of P is positive, we prove existence and regularity of a global solution provided that jj < C<, where C depends on K and N.

We consider a model arising from biology, consisting of chemotaxis equations coupled to viscous incompressible fluid equations through transport and external forcing. Global existence of solutions to the Cauchy problem is investigated under certain conditions. Precisely, for the chemotaxis–Navier–Stokes system in two space dimensions, we obtain global existence for large data. In three space di...

‎In this paper‎, ‎we consider the existence and uniqueness of the global solution for the sixth-order damped Boussinesq equation‎. ‎Moreover‎, ‎the finite-time blow-up of the solution for the equation is investigated by the concavity method‎.

This work is devoted to the study of global solution for initial value problem of interval fractional integrodifferential equations involving Caputo-Fabrizio fractional derivative without singular kernel admitting only the existence of a lower solution or an upper solution. Our method is based on fixed point in partially ordered sets. In this study, we guaranty the existence of special kind of ...