Global existence and uniqueness of strong solutions for the magnetohydrodynamic equations.
Global existence for a nonlinear Schroedinger–Chern–Simons system on a surface
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 for the inflow-outflow problem for the Navier-Stokes equations in a cylinder
Global existence of regular solutions to the Navier-Stokes equations describing the motion of an incompressible viscous fluid in a cylindrical pipe with large inflow and outflow is shown. To prove the long time existence we need smallness of derivatives, with respect to the variable along the axis of the cylinder, of the external force and of the initial velocity in L₂-norms. Moreover, we need smallness of derivatives of inflow and outflow with respect to tangent directions to the boundary and with...
Global existence for the nonlinear equations of crystal optics
Global existence for the Vlasov-Poisson equation in 3 space variables with small initial data
Global existence of 2D slightly compressible viscous magneto-fluid motion.
Global existence of axially symmetric solutions to Navier-Stokes equations with large angular component of velocity
Global existence of axially symmetric solutions to the Navier-Stokes equations in a cylinder with the axis of symmetry removed is proved. The solutions satisfy the ideal slip conditions on the boundary. We underline that there is no restriction on the angular component of velocity. We obtain two kinds of existence results. First, under assumptions necessary for the existence of weak solutions, we prove that the velocity belongs to , so it satisfies the Serrin condition. Next, increasing regularity...
Global existence of large amplitude solutions for nonlinear massless Dirac equation
Global existence of small classical solutions to nonlinear Schrödinger equations
Global existence of small radially symmetric solutions to quadratic nonlinear evolution equations in an exterior domain.
Global existence of smooth solutions for the Vlasov-Fokker-Planck equation in and space dimensions
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 for the 1-D radiative and reactive viscous gas dynamics
In this paper, we prove the existence of a global solution to an initial-boundary value problem for 1-D flows of the viscous heat-conducting radiative and reactive gases. The key point here is that the growth exponent of heat conductivity is allowed to be any nonnegative constant; in particular, constant heat conductivity is allowed.
Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case
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 existence of solutions to Navier-Stokes equations in cylindrical domains
We prove the existence of global and regular solutions to the Navier-Stokes equations in cylindrical type domains under boundary slip conditions, where coordinates are chosen so that the x₃-axis is parallel to the axis of the cylinder. Regular solutions have already been obtained on the interval [0,T], where T > 0 is large, on the assumption that the L₂-norms of the third component of the force field, of derivatives of the force field, and of the velocity field with respect to the direction of...
Global existence of solutions to Schrödinger equations on compact riemannian manifolds below
In this paper, we will study global well-posedness for the cubic defocusing nonlinear Schrödinger equations on the compact Riemannian manifold without boundary, below the energy space, i.e. , under some bilinear Strichartz assumption. We will find some , such that the solution is global for .