Dissipation and Dispersion Approximation to Hydrodynamical Equations and Asymptotic Limit (Journal of Partial Differential Equations, 2008)
The compressible Euler equations with dissipation and/or dispersion correction are widely used in the area of applied sciences, for instance, plasma physics, charge transport in semiconductor devices, astrophysics, geophysics, etc. We consider the compressible Euler equation with density-dependent (degenerate) viscosities and capillarity, and investigate the global existence of weak solutions and asymptotic limit.
Keywords: Hydrodynamics; degenerate viscosities; dispersion limit