We study the well-posedness of the Hele-Shaw-Cahn-Hilliard system modeling binary fluid flow in porous media with arbitrary viscosity contrast but matched density between the components.â€¦ (More)

almost surely has pure point spectrum with exponentially localized eigenfunctions. In d â‰¥ 2, it is known [FS, vDK, AM] that for 0 < Ç«1 â‰ª 1 almost surely the spectrum is pure point with exponentiallyâ€¦ (More)

In this paper, we prove the local well-posedness of the Ericksen-Leslie system, and the global well-posednss for small initial data under the physical constrain condition on the Leslie coefficients,â€¦ (More)

In this paper, we prove the local well-posedness in critical Besov spaces for the compressible Navier-Stokes equations with density dependent viscosities under the assumption that the initial densityâ€¦ (More)

Motivated by [P. Constantin, N. Masmoudi, Global well-posedness for a Smoluchowski equation coupled with Navierâ€“Stokes equations in 2D, Comm. Math. Phys. 278 (2008) 179â€“191; F. Lin, Ping Zhang,â€¦ (More)

In this paper, we prove the nonlinear orbital stability of the stationary traveling wave of the one-dimensional Gross-Pitaevskii equation by using Zakharov-Shabatâ€™s inverse scattering method.

In this paper, we prove the local well-posedness for the Ideal MHD equations in the Triebel-Lizorkin spaces and obtain blow-up criterion of smooth solutions. Specially, a recovered proof of [7] forâ€¦ (More)

We investigate the well-posedness for the 2D viscous shallow water equations in the theory of compressible fluid. Making use of the Fourier frequency localization and Bony paraproduct decomposition,â€¦ (More)

We present a rigorous derivation of the Ericksen-Leslie equation starting from the Doi-Onsager equation. As in the fluid dynamic limit of the Boltzmann equation, we first make the Hilbert expansionâ€¦ (More)