15 research outputs found
Weak solutions to problems involving inviscid fluids
We consider an abstract functional-differential equation derived from the
pressure-less Euler system with variable coefficients that includes several
systems of partial differential equations arising in the fluid mechanics. Using
the method of convex integration we show the existence of infinitely many weak
solutions for prescribed initial data and kinetic energy
The sharp-interface limit for the Navier--Stokes--Korteweg equations
We investigate the sharp-interface limit for the Navier--Stokes--Korteweg model, which is an extension of the compressible Navier--Stokes equations. By means of compactness arguments, we show that solutions of the Navier--Stokes--Korteweg equations converge to solutions of a physically meaningful free-boundary problem. Assuming that an associated energy functional converges in a suitable sense, we obtain the sharp-interface limit at the level of weak solutions
Existence of weak solution for compressible fluid models of Korteweg type
This work is devoted to prove existence of global weak solutions for a
general isothermal model of capillary fluids derived by J.- E Dunn and J.
Serrin (1985) [6], which can be used as a phase transition model. We improve
the results of [5] by showing the existence of global weak solution in
dimension two for initial data in the energy space, close to a stable
equilibrium and with specific choices on the capillary coefficients. In
particular we are interested in capillary coefficients approximating a constant
capillarity coefficient. To finish we show the existence of global weak
solution in dimension one for a specific type of capillary coefficients with
large initial data in the energy space
The Sharp-Interface Limit for the Navier–Stokes–Korteweg Equations
We investigate the sharp-interface limit for the Navier–Stokes–Korteweg model, which is an extension of the compressible Navier–Stokes equations. By means of compactness arguments, we show that solutions of the Navier–Stokes–Korteweg equations converge to solutions of a physically meaningful free-boundary problem. Assuming that an associated energy functional converges in a suitable sense, we obtain the sharp-interface limit at the level of weak solutions