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5 papers · 1 filter
Parabolic equations with variably partially VMO coefficients
Hongjie Dong
We prove the -solvability of second order parabolic equations in nondivergence form in the whole space for . The leading coefficients are assumed to b…
A regularity criterion for the dissipative quasi-geostrophic equations
Hongjie Dong, Natasa Pavlovic
We establish a regularity criterion for weak solutions of the dissipative quasi-geostrophic equations in mixed time-space Besov spaces.
On the Green's matrices of strongly parabolic systems of second order
Sungwon Cho, Hongjie Dong, Seick Kim
We establish existence and various estimates of fundamental matrices and Green's matrices for divergence form, second order strongly parabolic systems in arbitrary cylindrical doma…
Lorentz Space Estimates and Jacobian Convergence for the Ginzburg-Landau Energy with Applied Magnetic Field
Ian Tice
In this paper we continue the study of Lorentz space estimates for the Ginzburg-Landau energy started in our previous paper, \cite{p1}. We focus on getting estimates for the Ginzbu…
Pattern formation (I): The Keller-Segel Model
Yan Guo, Hyung Ju Hwang
We investigate nonlinear dynamics near an unstable constant equilibrium in the classical Keller-Segel model. Given any general perturbation of magnitude , we prove that its nonl…