Related papers: Global Well-Posedness for the Microscopic FENE Mod…
The FENE dumbbell model consists of the incompressible Navier-Stokes equation and the Fokker-Planck equation for the polymer distribution. In such a model, the polymer elongation cannot exceed a limit $\sqrt{b}$, yielding all interesting…
We consider the FENE dumbbell polymer model which is the coupling of the incompressible Navier-Stokes equations with the corresponding Fokker-Planck-Smoluchowski di ffusion equation. We show global well-posedness in the case of a 2D bounded…
We show the existence of global-in-time weak solutions to a general class of coupled FENE-type bead-spring chain models that arise from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The…
We consider the Cauchy problem to the 3D barotropic compressible Navier-Stokes equation. We prove global well-posedness, assuming that the initial data $(\rho_0-1,u_0)$ has small norms in the critical Besov space…
We prove the existence of global-in-time weak solutions to a general class of models that arise from the kinetic theory of dilute solutions of nonhomogeneous polymeric liquids, where the polymer molecules are idealized as bead-spring chains…
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…
We consider the incompressible and stationary Stokes equations on an infinite two-dimensional wedge with non-scaling invariant Navier-slip boundary conditions. We prove well-posedness and higher regularity of the Stokes problem in a certain…
A kinetic-fluid model describing the evolutions of disperse two-phase flows is considered. The model consists of the Vlasov-Fokker-Planck equation for the particles (disperse phase) coupled with the compressible Navier-Stokes equations for…
This paper investigates the local existence and uniqueness of strong solutions to the three-dimensional compressible Navier-Stokes equations with density-dependent viscosities in exterior domains. When both the shear and bulk viscosity…
We show the existence of global-in-time weak solutions to a general class of coupled bead-spring chain models that arise from the kinetic theory of dilute solutions of nonhomogeneous polymeric liquids with noninteracting polymer chains,…
We prove the existence of large-data global-in-time weak solutions to a general class of coupled bead-spring chain models with finitely extensible nonlinear elastic (FENE) type spring potentials for nonhomogeneous incompressible dilute…
In this paper, we consider the Keller--Segel--Navier--Stokes system with nonlinear boundary conditions in a bounded smooth (and not necessarily convex) domain $\Omega \subset \mathbb{R}^N$, $N \ge 2$, where the chemotactic sensitivity $S$…
This paper investigates an initial boundary value problem for the relaxed one-dimensional compressible Navier-Stokes-Fourier equations. By transforming the system into Lagrangian coordinates, the resulting formulation exhibits a uniform…
We investigate the global existence of weak solutions to a free boundary problem governing the evolution of finitely extensible bead-spring chains in dilute polymers. We construct weak solutions of the two-phase model by performing the…
The incompressible Navier-Stokes equations coupled to the Maxwell-Stefan relations for the molar fluxes are analyzed in bounded domains with no-flux boundary conditions. The system models the dynamics of a multicomponent gaseous mixture…
This paper shows that the Stokes problem is well-posed when velocity and pressure simultaneously vanish on the domain boundary. This result is achieved by extending Ne\v{c}as' inequality to square-integrable functions that vanish in a small…
In this paper we mainly investigate the Cauchy problem of the finite extensible nonlinear elastic (FENE) dumbbell model with dimension $d\geq2$. We first proved the local well-posedness for the FENE model in Besov spaces by using the…
We establish the global well-posedness for two-dimensional inhomogeneous, incompressible, anisotropic Navier-Stokes systems. Two specific models are analyzed: one with partial dissipation (referred to as (AINS)) and one with only horizontal…
We first show local-in-time well-posedness of the compressible Navier-Stokes equations, assuming striated regularity while no other smoothness or smallness conditions on the initial density. With these local-in-time solutions served as…
In this work, we proved the existence of a unique global mild solution of the d-dimensional incompressible Navier-Stokes equations, for small initial data in Besov type spaces based on mixed-Lebesgue spaces; namely, mixed-norm…