Global solution to a Hopf equation and its application to non-strictly hyperbolic systems of conservation laws.
Global solution to the Cauchy problem of nonlinear thermodiffusion in a solid body
We consider the initial-value problem for a nonlinear hyperbolic-parabolic system of three coupled partial differential equations of second order describing the process of thermodiffusion in a solid body (in one-dimensional space). We prove global (in time) existence and uniqueness of the solution to the initial-value problem for this nonlinear system. The global existence is proved using time decay estimates for the solution of the associated linearized problem. Next, we prove an energy estimate...
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 and exponential decay for a nonlinear coupled system of beam equations of Kirchhoff type with memory in a domain with moving boundary.
Global solutions and finite time blow up for damped semilinear wave equations
Global solutions and quenching to a class of quasilinear parabolic equations.
Global solutions for a nonlinear hyperbolic equation with boundary memory source term.
Global solutions for a nonlinear wave equation with the -Laplacian operator.
Global solutions for a problem modeling the dynamics of a system of self-gravitating Brownian particles
Results on the global existence and uniqueness of variational solutions to an elliptic-parabolic problem occurring in statistical mechanics are provided.
Global solutions of a strongly coupled reaction-diffusion system with different diffusion coefficients.
Global solutions of multidimensional approximate Navier-Stokes equations of a viscous gas.
Global solutions of nonlinear parabolic equations
Global solutions of quasilinear systems of Klein–Gordon equations in 3D
We prove small data global existence and scattering for quasilinear systems of Klein-Gordon equations with different speeds, in dimension three. As an application, we obtain a robust global stability result for the Euler-Maxwell equations for electrons.
Global solutions of semilinear heat equations in Hilbert spaces.
Global solutions of the Cauchy problem for a viscous polytropic ideal gas
Global solutions of the equations of elastodynamics for incompressible materials.
Global solutions of the homogeneous complex Monge-Ampère equation and complex structures on the tangent bundle of Riemannian manifolds.
Global solutions of the relativistic Vlasov-Maxwell system of plasma physics [Book]
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.