On the well-posedness for the Euler-Korteweg model in several space dimensions S. Benzoni-Gavage, R. Danchin and S. Descombes June 8, 2005 Introduction We call Korteweg model a system of conservation laws governing the motion of liquid-vapor mixtures, which takes into account the surface tension of interfaces by means of a capillarity co- efficient; see [16] and [11] for the early developments of the theory of capillarity, and for instance [18, 9] for the derivation of the equations of motion. In this kind of model, the interfaces are not sharp fronts. Their width, even though extremely small for values of the capillarity compatible with the measured, physical surface tension, is nonzero. We call them diffuse interfaces. We are especially interested in non-dissipative isothermal models, in which the viscosity of the fluid is neglected and therefore the (extended) free energy, depending on the density and its gradient, is a conserved quantity. From the mathematical point of view, the resulting conservation law for the momentum of the fluid involves a third order, dispersive term but no parabolic smoothing effect. The system made up with the conservation of mass and of momentum is thus the compressible Euler system modified by the adjunction of the so-called Korteweg stress, and we call it the Euler-Korteweg model.
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- euler-korteweg model
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- variable coefficients
- additional dependent variable
- system
- schrodinger equation
- system involves