Linear stability of propagating phase boundaries in capillary fluids

Dynamical phase changes occurring along planar traveling waves in capillary fluids are considered. Their multi-dimensional stability, which is encoded in the spectrum of a third order variational differential operator, is add ressed by two approaches. On one hand, an original energy method is used to show that these diffuse interfaces are weakly stable, More precisely, the spectrum of the involved operator is found to coincide with the imaginary a xis. On the other hand, an Evans function technique reveals a bifurcation p henomenon about zero, the interpretation of which still needs some clarific ation. It is the counterpart of the surface waves exhibited in an earlier w ork far the corresponding sharp interfaces. (C) 2001 Elsevier Science B.V. All rights reserved.