Finite Energy Local Well-Posedness for the Yang–Mills–Higgs Equations in Lorenz Gauge

Local Well-posedness for Membranes in the Light Cone Gauge

In this paper we consider the classical initial value problem for the bosonic membrane in light cone gauge. A Hamiltonian reduction gives a system with one constraint, the area preserving constraint. The Hamiltonian evolution equations corresponding to this system, however, fail to be hyperbolic. Making use of the area preserving constraint, an equivalent system of evolution equations is found,...

Local Well-posedness of the Yang-mills Equation in the Temporal Gauge below the Energy Norm

We show that the Yang-Mills equation in three dimensions in the Temporal gauge is locally well-posed in Hs for s > 3/4 if the Hs norm is sufficiently small. The temporal gauge is slightly less convenient technically than the more popular Coulomb gauge, but has the advantage of uniqueness even for large initial data, and does not require solving a nonlinear elliptic problem. To handle the tempor...

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...

Local Well-posedness of Nonlinear Dispersive Equations on Modulation Spaces

By using tools of time-frequency analysis, we obtain some improved local well-posedness results for the NLS, NLW and NLKG equations with Cauchy data in modulation spaces M 0,s .

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