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Green's functions for parabolic systems of second order in time-varying domains
Dong, H.,Kim, S. AIM SCIENCES 2014 COMMUNICATIONS ON PURE AND APPLIED ANALYSIS Vol.13 No.4
We construct Green's functions for divergence form, second order parabolic systems in non-smooth time-varying domains whose boundaries are locally represented as graph of functions that are Lipschitz continuous in the spatial variables and 1/2-Holder continuous in the time variable, under the assumption that weak solutions of the system satisfy an interior Holder continuity estimate. We also derive global pointwise estimates for Green's function in such time-varying domains under the assumption that weak solutions of the system vanishing on a portion of the boundary satisfy a certain local boundedness estimate and a local Holder continuity estimate. In particular, our results apply to complex perturbations of a single real equation.
Fan, J.,Li, F.,Nakamura, G. AIM SCIENCES 2014 COMMUNICATIONS ON PURE AND APPLIED ANALYSIS Vol.13 No.4
In this paper we establish the global existence of strong solution to the density-dependent incompressible magnetohydrodynamic equations with vaccum in a bounded domain in R-2. Furthermore, the limit as the heat conductivity coefficient tends to zero is also obtained.