Global solutions of the Landau–Lifshitz–Baryakhtar equation

Global Solutions of the Hunter-Saxton Equation

We construct a continuous semigroup of weak, dissipative solutions to a nonlinear partial differential equations modeling nematic liquid crystals. A new distance functional, determined by a problem of optimal transportation, yields sharp estimates on the continuity of solutions with respect to the initial data. 1 Introduction In this paper we investigate the Cauchy problem

WAVELET SOLUTIONS OF THE KLEIN-GORDON EQUATION

Global Solutions of Einstein–dirac Equation

The conformal space M was introduced by Dirac in 1936. It is an algebraic manifold with a spin structure and possesses naturally an invariant Lorentz metric. By carefully studying the birational transformations of M, we obtain explicitly the transition functions of the spin bundle over M. Since the transition functions are closely related to the propagation in physics, we get a kind of solution...

Global Solutions of the Random Vortex Filament Equation

In this article we prove the existence of a global solution for the random vortex filament equation. Our work gives a positive answer to a question left open in recent publications: Berselli and Gubinelli [5] showed the existence of global solution for a smooth initial condition while Bessaih, Gubinelli, Russo [6] proved the existence of a local solution for a general initial condition. In this...

Global Periodic Solutions of the Nonlinear Wave Equation

where u and 4~ denote scalar functions on R 2, and g is a scalar function on R. We shall assume g and ff continuous, and we shall determine sufficient conditions in the form of inequalities to guarantee that problem (1) has continuous solutions. Thus, the solutions which we consider will be weak solutions in the sense of distributions. In terms of functional analysis and the alternative approac...