Well-posedness for chemotaxis–fluid models in arbitrary dimensions*

Well Posedness for Multilane Traffic Models

We give rigorous results on the analytical properties of multilane traffic flow models based on hyperbolic balance laws. 2000 Mathematics Subject Classification: 35L65, 35L67, 90B20

Exactly Solvable Models in Arbitrary Dimensions

We construct a new class of quasi-exactly solvable many-body Hamiltonians in arbitrary dimensions, whose ground states can have any correlations we choose. Some of the known correlations in one dimension and some recent novel correlations in two and higher dimensions are reproduced as special cases. As specific interesting examples, we also write down some new models in two and higher dimension...

Well-posedness for Hall-magnetohydrodynamics

We prove local existence of smooth solutions for large data and global smooth solutions for small data to the incompressible, resitive, viscous or inviscid Hall-MHD model. We also show a Liouville theorem for the stationary solutions. Acknowledgements: The first and third authors wish to thank the hospitality of the Institut de Mathématiques de Toulouse, France, where this research has been car...

Well-posedness for Hyperbolic Problems

Well-posedness for General 2

We consider the Cauchy problem for a strictly hyperbolic 2 2 system of conservation laws in one space dimension u t + F (u)] x = 0; u(0; x) = u(x); (1) which is neither linearly degenerate nor genuinely non-linear. We make the following assumption on the characteristic elds. If r i (u); i = 1; 2; denotes the i-th right eigenvector of DF (u) and i (u) the corresponding eigenvalue, then the set f...