## Journals

- Advances in Mathematics of Communications
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### Open Access Journals

DCDS

In this paper, we investigate the well-posedness of the Maxwell-Chern-Simons-Higgs
system in the Lorenz gauge. In particular, we prove that the system is globally wellposed
in the energy space. As an application, we prove that the solution of the Maxwell-Chern-Simons-Higgs
system converges to that of Maxwell-Higgs system in $H^s\times H^{s-1}$($s\geq1$) as the
Chern-Simons coupling constant $\kappa\rightarrow0$.

CPAA

In this paper, we investigate the dynamics of a boson gas with three-body interactions
in $T^2$. We prove that when the particle
number $N$ tends to infinity, the BBGKY hierarchy of $k$-particle marginals converges to a infinite
Gross-Pitaevskii(GP) hierarchy for which we prove uniqueness of solutions,
and for the asymptotically factorized $N$-body initial datum, we show that this $N\rightarrow\infty$ limit
corresponds to the quintic nonlinear Schrödinger equation.
Thus, the Bose-Einstein condensation is preserved in time.

DCDS

In this paper, we consider the Maxwell-Klein-Gordon and Maxwell-Chern-Simons-Higgs systems
in the temporal gauge. By using the fact that when the spatial gauge potentials are in the Coulomb gauge, their
$\dot{H}^1$ norms can be controlled by the energy of the corresponding system and their $L^2$ norms, and the gauge
invariance of the systems, we show that finite energy solutions of these two systems exist globally in this gauge.

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