In this pape,~ we study uniform L1-stability and asymptotic completeness of the Vlasov-Yukawa-Boltzmann （V-Y-B） system. For a sufficiently small rand smooth initial data, we show that classical solutions exist globa...In this pape,~ we study uniform L1-stability and asymptotic completeness of the Vlasov-Yukawa-Boltzmann （V-Y-B） system. For a sufficiently small rand smooth initial data, we show that classical solutions exist globally and satisfy dispersion estimates, uniform L1-stability with respect to initial data and scattering type estimate. We show that the short range nature of interactions due to the Yukawa potential enables us to construct robust Lyapunov type functional to derive scattering states. In the zero mass limit of force carrier particles, we also show that the classical solutions to the V-Y-B system converge to that of the Vlasov-Poisson-Boltzmann （V-P-B） system in any finite time interval展开更多
We study the large-time dynamics of Cucker-Smale(C-S)flocking particles interacting with nonNewtonian incompressible fluids.Dynamics of particles and fluids were modeled using the kinetic Cucker-Smale equation for par...We study the large-time dynamics of Cucker-Smale(C-S)flocking particles interacting with nonNewtonian incompressible fluids.Dynamics of particles and fluids were modeled using the kinetic Cucker-Smale equation for particles and non-Newtonian Navier-Stokes system for fluids,respectively and these two systems are coupled via the drag force,which is the main flocking(alignment)mechanism between particles and fluids.We present a global existence theory for weak solutions to the coupled Cucker-Smale-Navier-Stokes system with shear thickening.We also use a Lyapunov functional approach to show that sufficiently regular solutions approach flocking states exponentially fast in time.展开更多
In this paper we prove the uniform boundary Harnack principle in general open sets for harmonic functions with respect to a large class of rotationally symmetric purely discontinuous Levy processes.
基金partially supported by a National Research Foundation of Korea Grant funded by the Korean Government(2014R1A2A205002096)supported by BK21 Plus-KAIST
文摘In this pape,~ we study uniform L1-stability and asymptotic completeness of the Vlasov-Yukawa-Boltzmann （V-Y-B） system. For a sufficiently small rand smooth initial data, we show that classical solutions exist globally and satisfy dispersion estimates, uniform L1-stability with respect to initial data and scattering type estimate. We show that the short range nature of interactions due to the Yukawa potential enables us to construct robust Lyapunov type functional to derive scattering states. In the zero mass limit of force carrier particles, we also show that the classical solutions to the V-Y-B system converge to that of the Vlasov-Poisson-Boltzmann （V-P-B） system in any finite time interval
基金supported by the Samsung Science and Technology Foundation (Grant No. SSTF-BA1401-03)Hwa Kil Kim was supported by the National Research Foundation of Korea (Grant No. NRF2015R1D1A1A01056696)+1 种基金Jae-Myoung Kim was supported by BK21 PLUS SNU Mathematical Sciences Divisionthe National Research Foundation of Korea (Grant No. NRF-2016R1D1A1B03930422)
文摘We study the large-time dynamics of Cucker-Smale(C-S)flocking particles interacting with nonNewtonian incompressible fluids.Dynamics of particles and fluids were modeled using the kinetic Cucker-Smale equation for particles and non-Newtonian Navier-Stokes system for fluids,respectively and these two systems are coupled via the drag force,which is the main flocking(alignment)mechanism between particles and fluids.We present a global existence theory for weak solutions to the coupled Cucker-Smale-Navier-Stokes system with shear thickening.We also use a Lyapunov functional approach to show that sufficiently regular solutions approach flocking states exponentially fast in time.
基金supported by National Research Foundation of Korea (Grant No. 2011-0027230)supported in part by a grant from the Simons Foundation (Grant No. 208236)supportedin part by the MZOS Grant (Grant No. 037-0372790-2801)
文摘In this paper we prove the uniform boundary Harnack principle in general open sets for harmonic functions with respect to a large class of rotationally symmetric purely discontinuous Levy processes.
