Related papers: Small data global regularity for simplified 3-D Er…
The work deals with the Ericksen-Leslie model for nematic liquid crystals on the whole space, the half-space and on exterior domains with smooth boundary. The crystal orientation is described by a unit vector that is a small perturbation of…
Ericksen and Leslie proposed a hydrodynamic model for liquid crystals in the format of conservation laws in the 1960s. Their original model includes inertial and compressibility effects, which makes the model a coupled parabolic-hyperbolic…
We study an initial-boundary value problem for the incompressible Navier-Stokes-Cahn-Hilliard system with non-constant density proposed by Abels, Garcke and Gr\"{u}n in 2012. This model arises in the diffuse interface theory for binary…
In this work, we establish the global existence of strong solutions to the 2D and 3D compressible Navier-Stokes-Korteweg system with arbitrarily large initial data on the torus. This system was derived by Dunn and Serrin [Arch. Ration.…
In this paper we investigate a forced incompressible Navier-Stokes equation coupled with a parabolic type equation of Q-tensors in a domain $U\subset\R^3.$ In the case $U$ is bounded, we prove the existence of a global strong solution when…
In this paper, we study the long-time behavior of full Ericksen-Leslie system modeling the hydrodynamics of nematic liquid crystals between two dimensional unit spheres. Under a weaker assumption for Leslie's coefficients, we give the key…
This paper gives another version of results due to Raugel and Sell, and similar results due to Moise, Temam and Ziane, that state the following: the solution of the Navier-Stokes equation on a thin 3 dimensional domain with periodic…
The work deals with the Ericksen-Leslie System for nematic liquid crystals on the whole space. In our work we suppose the initial condition of the orientation field stays on an arc connecting two fixed orthogonal vectors on the unit sphere.…
We prove short time regularity of suitable weak solutions of 3D incompressible Navier-Stokes equations near a point where the initial data is locally in $L^3$. The result is applied to the regularity problems of solutions with uniformly…
In three previous papers by the two first authors, classes of initial data to the three dimensional, incompressible Navier-Stokes equations were presented, generating a global smooth solution although the norm of the initial data may be…
We prove a stability result of constant equilibria for the three-dimensional Navier-Stokes-Poisson system uniform in the inviscid limit. We allow the initial density to be close to a constant and the potential part of the initial velocity…
In this paper we study the global regularity for the solution to the Dirichlet problem of the equation of minimal graphs over a convex domain in hyperbolic spaces. We find that the global regularity depends only on the convexity of the…
We prove an $\epsilon$-regularity criterion for the 3D Navier-Stokes equations in terms of initial data. It shows that if a scaled local $L^2$ norm of initial data is sufficiently small around the origin, a suitable weak solution is regular…
This paper investigates the global dynamics of the Euler--Riesz system in three dimensions, focusing on the well-posedness and large-time behavior of solutions near equilibrium. The system generalizes classical interactions by incorporating…
We consider a coupled Wave-Klein-Gordon system in 3D, and prove global regularity and modified scattering for small and smooth initial data with suitable decay at infinity. This system was derived by Wang and LeFloch-Ma as a simplified…
We study the Ericksen-Leslie's hyperbolic incompressible liquid crystal model. Under some constraints on the Leslie coefficients which ensure the basic energy law is dissipative, we prove the local-in-time existence and uniqueness of the…
A classical 3-D thermoviscoelastic system of Kelvin-Voigt type is considered. The existence and uniqueness of a global regular solution is proved without small data assumption. The existence proof is based on the successive approximation…
In this paper, we consider a simplified Ericksen-Leslie model for the nematic liquid crystal flow. The evolution system consists of the Navier-Stokes equations coupled with a convective Ginzburg-Landau type equation for the averaged…
We study a nonlinear parabolic system for a time dependent solenoidal vector field on $\Bbb R^3$. The nonlinear term of this new model equations is obtained slightly modifying that of the Navier-Stokes equations. The system has the same…
We establish, for smooth enough initial data, the global well-posedness (existence, uniqueness and continuous dependence on initial data) of solutions, for an inviscid three-dimensional {\it slow limiting ocean dynamics} model. This model…