Existence of Global Weak Solution for Compressible Fluid Models of Korteweg Type
By Boris Haspot. 2009
139 citations recorded by the source corpus.
This work is devoted to proving existence of global weak solutions for a general isothermal model of capillary fluids derived by Dunn and Serrin (Arch Rational Mech Anal 88(2):95–133, 1985) which can be used as a phase transition model. We improve the results of Danchin and Desjardins (Annales de l’IHP, Analyse non linéaire 18:97–133, 2001) 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 κ. 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.
Subfields: Applied Mathematics, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/610c06869aa55d36cd1097e0d420653fb78bd4e5
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In Applied Mathematics
In Control and Systems Engineering
Citations in the corpus
- Existence and nonlinear stability of stationary solutions to the full compressible Navier–Stokes–Korteweg system (2014, background): “Bresch, Desjardins and Lin [8] showed the global existence of weak solution to the compressible fluid models of Korteweg type, then Haspot improved their results in [9].”
- Existence and time-asymptotics of global strong solutions to dynamic Korteweg models (2014, background): “In [15], Haspot considers the Korteweg model for the dimensions N = 2, N = 1 and specific capillarity coefficients.”