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Global well-posedness of the partially damped 2D MHD equations via a direct normal mode method for the anisotropic linear operator
Min Jun Jo, Junha Kim, Jihoon Lee
We prove the global well-posedness of the 2D incompressible non-resistive MHD equations with a velocity damping term near the non-zero constant background magnetic field. To this e…
Global well-posedness of logarithmic Keller-Segel type systems
Jaewook Ahn, Kyungkeun Kang, Jihoon Lee
We consider a class of logarithmic Keller-Segel type systems modeling the spatio-temporal behavior of either chemotactic cells or criminal activities in spatial dimensions two and…
Nonlocal adhesion models for two cancer cell phenotypes in a multidimensional bounded domain
Jaewook Ahn, Myeongju Chae, Jihoon Lee
Cell-cell adhesion is an inherently nonlocal phenomenon. Numerous partial differential equation models with nonlocal term have been recently presented to describe this phenomenon,…
Global Well-posedness and Long Time Behaviors of Chemotaxis-Fluid System Modeling Coral Fertilization
Myeongju Chae, Kyungkeun Kang, Jihoon Lee
We consider generalized models on coral broadcast spawning phenomena involving diffusion, advection, chemotaxis, and reactions when egg and sperm densities are different. We prove…
Global existence and temporal decay in Keller-Segel models coupled to fluid equations
Myeongju Chae, Kyungkeun Kang, Jihoon Lee
We consider a Keller-Segel model coupled to the incompressible Navier-Stokes equations in spatial dimensions two and three. We establish the local existence of regular solutions an…