相关论文: Local Well-Posedness for Relaxational Fluid Vesicl…
We consider image registration as an optimal control problem using an optical flow formulation, i.e., we discuss an optimization problem that is governed by a linear hyperbolic transport equation. Requiring Lipschitz continuity of the…
In this paper, we continue the study of the local well-posedness theory for the Schr\"{o}dinger-KdV system in the Sobolev space $H^{s_1}\times H^{s_2}$. We show the local well-posedness in $H^{-3/16}\times H^{-3/4}$ for $\beta = 0$.…
We prove short-time well-posedness and existence of global weak solutions of the Beris--Edwards model for nematic liquid crystals in the case of a bounded domain with inhomogeneous mixed Dirichlet and Neumann boundary conditions. The system…
In this article we consider a fluid-structure interactions model on a three dimensional bounded domain, that describes the mechanical interaction between blood flow and a thrombus with Hookean elasticity. The interface between the two…
We prove the local well-posedness of the 3D free-boundary incompressible ideal magnetohydrodynamics (MHD) equations with surface tension, which describe the motion of a perfect conducting fluid in an electromagnetic field. We adapt the…
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 density is bounded away from zero.
In this work, we consider the interaction of a 3D incompressible fluid with a 2D flexible shell that occupies (a part of) the boundary of the fluid domain. We assume that the shell is perfectly elastic while the fluid is governed by the…
We study the problem of the motion of the free surface of a compressible fluid. We prove existence for the linearized equations.
We study the local and global wellposedness of a full system of Magneto-Hydro-Dynamic equations. The system is a coupling of the forced (Lorentz force) incompressible Navier-Stokes equations with the Maxwell equations through Ohm's law for…
The MMT equation was proposed by Majda, McLaughlin and Tabak as a model to study wave turbulence. We focus on the kinetic equation associated to this Hamiltonian system, which is believed to give a way to predict turbulent spectra. We…
We consider a free boundary problem of the Navier--Stokes equations in the three-dimensional Euclidean space with moving contact line, where the 90$^\circ$-contact angle condition is posed. We show that for given $T > 0$ the problem is…
In this paper, we consider the full compressible, viscous, non-resistive MHD system under the assumption that the fluids move on a plane while the magnetic field is oriented vertically. Within the framework of Besov spaces, by introducing…
In this article, we prove the local well-posedness of the free-boundary Lin-Liu equations describing the motion of inviscid nematic liquid crystals in the presence of surface tension in Lagrangian coordinates. It is well known that a priori…
The Hall-magnetohydrodynamics (Hall-MHD) equations, rigorously derived from kinetic models, are useful in describing many physical phenomena in geophysics and astrophysics. This paper studies the local well-posedness of classical solutions…
Concentration-compactness is used to prove compactness of maximising sequences for a variational problem governing symmetric steady vortex-pairs in a uniform planar ideal fluid flow, where the kinetic energy is to be maximised and the…
The initial-value problem for a particular bidirectional Whitham system modelling surface water waves is under consideration. This system was recently introduced in [4]. It is numerically shown to be stable and a good approximation to the…
We establish linearized well-posedness of the Triple-Deck system in Gevrey-$\frac32$ regularity in the tangential variable, under concavity assumptions on the background flow. Due to the recent result \cite{DietertGV}, one cannot expect a…
We consider a state-of-the-art ferroelectric phase-field model arising from the engineering area in recent years, which is mathematically formulated as a coupled elliptic-parabolic differential system. We utilize a fixed point theorem based…
We introduce a class of continuum mechanical models aimed at describing the behaviour of viscoelastic fluids by incorporating concepts originated in the theory of solid plasticity. Within this class, even a simple model with constant…
We consider the free boundary problem for a layer of compressible viscous barotropic fluid lying above a fixed rigid bottom and below the atmosphere of positive constant pressure. The fluid dynamics is governed by the compressible…