Global existence and blow-up for a shallow water equation
Global existence and extinction of weak solutions to a class of semiconductor equations with fast diffusion terms.
Global existence and one-dimensional nonlinear stability of shearing motions of viscoelastic fluids of Oldroyd type
Global existence and uniqueness of strong solutions for the magnetohydrodynamic equations.
Global existence for a one-dimensional model in gas dynamics
We prove the existence of a global solution for a one-dimensio- nal Navier-Stokes system for a gas with internal capillarity.
Global existence for a system of nonlocal PDEs with applications to chemically reacting incompressible fluids
We show global existence for a class of models of fluids that change their properties depending on the concentration of a chemical. We allow that the stress tensor in (t, x) depends on the velocity and concentration at other points and times. The example we have in mind foremost are materials with memory.
Global existence of 2D slightly compressible viscous magneto-fluid motion.
Global existence of solutions for incompressible magnetohydrodynamic equations
Global-in-time existence of solutions for incompressible magnetohydrodynamic fluid equations in a bounded domain Ω ⊂ ℝ³ with the boundary slip conditions is proved. The proof is based on the potential method. The existence is proved in a class of functions such that the velocity and the magnetic field belong to and the pressure q satisfies for p ≥ 7/3.
Global existence of solutions of the free boundary problem for the equations of magnetohydrodynamic compressible fluid
Global existence of solutions for equations describing a motion of magnetohydrodynamic compresible fluid in a domain bounded by a free surface is proved. In the exterior domain we have an electromagnetic field which is generated by some currents located on a fixed boundary. We have proved that the domain occupied by the fluid remains close to the initial domain for all time.
Global mild solutions of the micropolar fluid system in critical spaces
We prove the global in time existence of a small solution for the 3D micropolar fluid system in critical Fourier-Herz spaces by using the Fourier localization method and Littlewood-Paley theory.
Global regularity for the 3D MHD system with damping
We study the Cauchy problem for the 3D MHD system with damping terms and (ε, δ > 0 and α, β ≥ 1), and show that the strong solution exists globally for any α, β > 3. This improves the previous results significantly.
Global solution of viscous compressible barotropic multipolar gas in a finite channel with nonzero input and output
The paper contains the proof of global existence of weak solutions of the viscous compressible barotropic gas for the initial-boundary value problem in a finite channel.
Global solution to the ideal compressible heat conductive multipolar fluid
Global solution to the isothermal compressible bipolar fluid in a finite channel with nonzero input and output
The paper contains the proof of global existence of weak solutions viscous compressible isothermal bipolar fluid of initial boundary value in a finite channel.
Global solutions of the Cauchy problem for a viscous polytropic ideal gas
Global solutions to vortex density equations arising from sup-conductivity
Global strong solutions of a 2-D new magnetohydrodynamic system
The main objective of this paper is to study the global strong solution of the parabolic-hyperbolic incompressible magnetohydrodynamic model in the two dimensional space. Based on Agmon, Douglis, and Nirenberg’s estimates for the stationary Stokes equation and Solonnikov’s theorem on --estimates for the evolution Stokes equation, it is shown that this coupled magnetohydrodynamic equations possesses a global strong solution. In addition, the uniqueness of the global strong solution is obtained.
Global well-posedness for the 2-D Boussinesq system with temperature-dependent thermal diffusivity
We prove the global well-posedness of the 2-D Boussinesq system with temperature dependent thermal diffusivity and zero viscosity coefficient.
Global well-posedness for the 2D quasi-geostrophic equation in a critical Besov space.
Global well-posedness for the primitive equations with less regular initial data
This paper is devoted to the study of the lifespan of the solutions of the primitive equations for less regular initial data. We interpolate the globall well-posedness results for small initial data in given by the Fujita-Kato theorem, and the result from [6] which gives global well-posedness if the Rossby parameter is small enough, and for regular initial data (oscillating part in and quasigeostrophic part in ).