Formation of singularity for compressible viscoelasticity

Singularity formation for compressible Euler equations

In this paper, for the p-system and full compressible Euler equations in one space dimension, we provide an equivalent and a sharp condition on initial data, respectively, under which the classical solution must break down in finite time. Moreover, we provide time-dependent lower bounds on density for arbitrary classical solutions for these two equations. Our results have no restriction on the ...

Compressible viscoelasticity: stability of solutions for homogeneous plane-Earth models

Formation of singularity and smooth wave propagation for the non-isentropic compressible Euler equations

We define compressive and rarefactive waves and give the differential equations describing smooth wave steepening for the compressible Euler equations with a varying entropy profile and general pressure laws. Using these differential equations, we directly generalize P. Lax’s singularity (shock) formation results in [9] for hyperbolic systems with two variables to the 3× 3 compressible Euler eq...

Well-posedness for compressible Euler equations with physical vacuum singularity

An important problem in the theory of compressible gas flows is to understand the singular behavior of vacuum states. The main difficulty lies in the fact that the system becomes degenerate at the vacuum boundary, where the characteristics coincide and have unbounded derivative. In this paper, we overcome this difficulty by presenting a new formulation and new energy spaces. We establish the lo...

simulation and experimental studies for prediction mineral scale formation in oil field during mixing of injection and formation water

abstract: mineral scaling in oil and gas production equipment is one of the most important problem that occurs while water injection and it has been recognized to be a major operational problem. the incompatibility between injected and formation waters may result in inorganic scale precipitation in the equipment and reservoir and then reduction of oil production rate and water injection rate. ...