http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
A regularity condition and temporal asymptotics for chemotaxis-fluid equations
Chae, Myeongju,Kang, Kyungkeun,Lee, Jihoon,Lee, Ki-Ahm Institute of Physics and the London Mathematical S 2018 Nonlinearity Vol.31 No.2
<P>We consider two dimensional chemotaxis equations coupled to the Navier–Stokes equations. We present a new localized regularity criterion that is localized in a neighborhood at each point. Secondly, we establish temporal decays of the regular solutions under the assumption that the initial mass of biological cell density is sufficiently small. Both results are improvements of previously known results given in Chae <I>et al</I> (2013 <I>Discrete Continuous Dyn. Syst</I>. A <B>33</B> 2271–97) and Chae <I>et al</I> (2014 <I>Commun. PDE</I> <B>39</B> 1205–35)</P>
The stability of nonlinear Schrödinger equations with a potential in high Sobolev norms revisited
Chae, Myeongju,Kwon, Soonsik AIM SCIENCES 2016 COMMUNICATIONS ON PURE AND APPLIED ANALYSIS Vol.15 No.2
<P>We consider the nonlinear Schrodinger equations with a potential on T-d. For almost all potentials, we show the almost global stability in very high Sobolev norms. We apply an iteration of the Birkhoff normal form, as in the formulation introduced by Bourgain [4]. This result reproves a dynamical consequence of the infinite dimensional Birkhoff normal form theorem by Bambusi and Grebert [2].</P>
Time-asymptotic behavior of the Vlasov–Poisson–Boltzmann system near vacuum
Chae, Myeongju,Ha, Seung-Yeal,Hwang, Hyung Ju Elsevier 2006 Journal of differential equations Vol.230 No.1
<P><B>Abstract</B></P><P>We present a collision potential for the Vlasov–Poisson–Boltzmann system near vacuum in plasma physics case. This potential measures the future possible collisions between charged particles with different velocities and satisfies a time-decay estimate. We use this time-decay property of the functional to show that the dynamics of the Vlasov–Poisson–Boltzmann is time-asymptotically equivalent to that of the corresponding linear Vlasov equation, when initial datum is small and decays fast enough in phase space as in [Y. Guo, The Vlasov–Poisson–Boltzmann system near vacuum, Comm. Math. Phys. 218 (2001) 293–313].</P>
Chae, Myeongju,Kang, Kyungkeun,Lee, Jihoon Elsevier 2011 Journal of differential equations Vol.251 No.9
<P><B>Abstract</B></P><P>We consider a system coupling the incompressible Navier–Stokes equations to the Vlasov–Fokker–Planck equation. The coupling arises from a drag force exerted by each other. We establish existence of global weak solutions for the system in two and three dimensions. Furthermore, we obtain the existence and uniqueness result of global smooth solutions for dimension two. In case of three dimensions, we also prove that strong solutions exist globally in time for the Vlasov–Stokes system.</P>
NONRELATIVISTIC LIMIT OF CHERN-SIMONS GAUGED FIELD EQUATIONS
Chae, Myeongju,Yim, Jihyun Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.3
We study the nonrelativistic limit of the Chern-Simons-Dirac system on ${\mathbb{R}}^{1+2}$. As the light speed c goes to infinity, we first prove that there exists an uniform existence interval [0, T] for the family of solutions ${\psi}^c$ corresponding to the initial data for the Dirac spinor ${\psi}_0^c$ which is bounded in $H^s$ for ${\frac{1}{2}}$ < s < 1. Next we show that if the initial data ${\psi}_0^c$ converges to a spinor with one of upper or lower component zero in $H^s$, then the Dirac spinor field converges, modulo a phase correction, to a solution of a linear $Schr{\ddot{o}}dinger$ equation in C([0, T]; $H^{s^{\prime}}$) for s' < s.