Global solutions, structure of initial data and the Navier-Stokes equations
In this note we present a proof of existence of global in time regular (unique) solutions to the Navier-Stokes equations in an arbitrary three dimensional domain with a general boundary condition. The only restriction is that the L₂-norm of the initial datum is required to be sufficiently small. The magnitude of the rest of the norm is not restricted. Our considerations show the essential role played by the energy bound in proving global in time results for the Navier-Stokes equations.
Global solutions to vortex density equations arising from sup-conductivity
Global solutions with infinite energy for the one-dimensional Zakharov system.
Global special regular solutions to the Navier-Stokes equations in axially symmetric domains under boundary slip conditions [Book]
Global strong solution and its decay properties for the Navier-Stokes equations in three dimensional domains with non-compact boundaries.
Global strong solution of the Navier-Stokes equations in 4 and 5 dimensional unbounded domains
Global strong solutions in Sobolev or Lebesgue spaces to the incompressible Navier-Stokes equations in
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 strong solutions of Vlasov's equation---necessary and sufficient conditions for their existence
Global weak solutions of the Navier-Stokes equations with nonhomogeneous boundary data and divergence
Global weak solvability of a regularized system of the Navier-Stokes equations for compressible fluid
The paper contains the proof of global existence of weak solutions to the mixed initial-boundary value problem for a certain modification of a system of equations of motion of viscous compressible fluid. The modification is based on an application of an operator of regularization to some terms appearing in the system of equations and it does not contradict the laws of fluid mechanics. It is assumed that pressure is a known function of density. The method of discretization in time is used and finally,...
Global weak solvability to the regularized viscous compressible heat conductive flow
The concept of regularization to the complete system of Navier-Stokes equations for viscous compressible heat conductive fluid is developed. The existence of weak solutions for the initial boundary value problem for the modified equations is proved. Some energy and etropy estimates independent of the parameter of regularization are derived.
Global well-posedness and blow up for the nonlinear fractional beam equations
We establish the Strichartz estimates for the linear fractional beam equations in Besov spaces. Using these estimates, we obtain global well-posedness for the subcritical and critical defocusing fractional beam equations. Of course, we need to assume small initial data for the critical case. In addition, by the convexity method, we show that blow up occurs for the focusing fractional beam equations with negative energy.
Global well-posedness and scattering for the defocusing -subcritical Hartree equation in
Global well-posedness and scattering for the derivative nonlinear Schrödinger equation with small rough data
Global well-posedness and scattering for the higher-dimensional energy-critical nonlinear Schrödinger equation for radial data.
Global well-posedness for KdV in Sobolev spaces of negative index.
Global well-posedness for Schrödinger equations with derivative in a nonlinear term and data in low-order Sobolev spaces.
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.