Well-posedness of phase-lock equations of superconductivity

Backward Uniqueness of Phase-Lock Equations of Superconductivity

In this article we will show that the phase-pock equations of Superconductivity have backward uniqueness. Backward uniqueness guarantees that the semi group generated by the solutions of phase-lock equations is injective, which plays an important role in understanding the long time dynamic properties of the solutions. INTRODUCTION In the previous article [1-3], we proposed the following phase-l...

Well-posedness of modified Camassa–Holm equations

Article history: Received 4 April 2008 Revised 11 January 2009 Available online 28 February 2009

Well-posedness of the Water-waves Equations

1.1. Presentation of the problem. The water-waves problem for an ideal liquid consists of describing the motion of the free surface and the evolution of the velocity field of a layer of perfect, incompressible, irrotational fluid under the influence of gravity. In this paper, we restrict our attention to the case when the surface is a graph parameterized by a function ζ(t,X), where t denotes th...

Well-posedness for the Navier-Stokes equations

where u is the velocity and p is the pressure, with inital data u(x, 0) = u0(x). Existence of weak solutions has been shown by Leray. Uniqueness (and regularity) of weak solutions is unknown and both are among the major open questions in applied analysis. Under stronger assumptions there exist local and/or global smooth solutions. One version of this has been shown by Kato for initial data in L...

WELL- POSEDNESS OF THE ROTHE DIFFERENCE SCHEME FOR REVERSE PARABOLIC EQUATIONS