Well-posedness for thermo-electro-viscoelasticity of Green–Naghdi type

Well-Posedness for Semi-Relativistic Hartree Equations of Critical Type

We prove local and global well-posedness for semi-relativistic, nonlinear Schrödinger equations i∂tu = √ −∆+ mu+F (u) with initial data in H(R), s ≥ 1/2. Here F (u) is a critical Hartree nonlinearity that corresponds to Coulomb or Yukawa type self-interactions. For focusing F (u), which arise in the quantum theory of boson stars, we derive a sufficient condition for global-in-time existence in ...

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...

Dynamic Coupled Thermo-Viscoelasticity of a Spherical Hollow Domain

The generalized coupled thermo-viscoelasticity of hollow sphere subjected to thermal symmetric shock load is presented in this paper. To overcome the infinite speed of thermal wave propagation, the Lord-Shulman theory is considered. Two coupled equations, namely, the radial equation of motion and the energy equation of a hollow sphere are obtained in dimensionless form. Resulting equations are ...