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Global existence for nonlinear system of wave equations in 3-D domains

Jianwei Yang (2011)

Applicationes Mathematicae

We study the initial-boundary problem for a nonlinear system of wave equations with Hamilton structure under Dirichlet's condition. We use the local-in-time Strichartz estimates from [Burq et al., J. Amer. Math. Soc. 21 (2008), 831-845], Morawetz-Pohožaev's identity derived in [Miao and Zhu, Nonlinear Anal. 67 (2007), 3136-3151], and an a priori estimate of the solutions restricted to the boundary to show the existence of global and unique solutions.

Global existence for the inflow-outflow problem for the Navier-Stokes equations in a cylinder

Piotr Kacprzyk (2009)

Applicationes Mathematicae

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 of axially symmetric solutions to Navier-Stokes equations with large angular component of velocity

Wojciech M. Zajączkowski (2004)

Colloquium Mathematicae

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 W 4 / 3 2 , 1 ( Ω × ( 0 , T ) ) , so it satisfies the Serrin condition. Next, increasing regularity...

Global existence of solutions for a strongly coupled population system

Gonzalo Galiano, Ansgar Jüngel (2003)

Banach Center Publications

A strongly coupled cross-diffusion model for two competing species in a heterogeneous environment is analyzed. We sketch the proof of an existence result for the evolution problem with non-flux boundary conditions in one space dimension, completing previous results [4]. The proof is based on a symmetrization of the problem via an exponential transformation of variables and the use of an entropy functional.

Global existence of solutions for incompressible magnetohydrodynamic equations

Wisam Alame, W. M. Zajączkowski (2004)

Applicationes Mathematicae

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 W p 2 , 1 ( Ω × ( 0 , T ) ) and the pressure q satisfies ∇ q ∈ L p ( Ω × ( 0 , T ) ) for p ≥ 7/3.

Currently displaying 261 – 280 of 479