Related papers: How strongly does diffusion or logistic-type degra…
In this article, we study the non-uniqueness of weak solutions for the two-dimensional hyper-dissipative Navier-Stokes equations in the super-critical spaces $L_{t}^{\gamma}W_{x}^{s,p}$ when $\alpha\in[1,\frac{3}{2})$, and obtain the…
In this paper, the system of particles coupled with fluid is considered. The particles are described by a Vlasov equation, and the fluid is governed by a forced Navier-Stokes equations. The interaction with fluid phase governed by…
We consider the global Cauchy problem for the generalized incompressible Navier- Stokes system in 3D whole space $$ u_t+u\cdot\nabla u+\nabla p=\mathcal{A}_h u, $$ \begin{equation}\label{main0} \nabla\cdot u=0, \end{equation} $$…
The present work deals with a Keller-Segel-Navier-Stokes system with potential consumption, under homogeneous Neumann boundary conditions for cell density and chemical signal, and of Dirichlet type for the velocity field, over a bounded…
We consider three dimensional incompressible Navier-Stokes equation $(NS)$ with different viscous coefficient in the vertical and horizontal variables. In particular, when one of these viscous coefficients is large enough compared to the…
We study a Navier-Stokes/Cahn-Hilliard system modeling the evolution of a compressible binary mixture of viscous fluids undergoing phase separation. The novelty of this work is a free energy potential including the physically relevant…
Global-in-time weak solutions to the Compressible Navier-Stokes-Poisson equations in a three-dimensional torus for large data are considered in this paper. The system takes into account density-dependent viscosity and non-monotone presseur.…
We study a complex non-newtonian fluid that models the flow of nematic liquid crystals. The fluid is described by a system that couples a forced Navier-Stokes system with a parabolic-type system. We prove the existence of global weak…
We study Cauchy problem of a class of viscous Camassa-Holm equations (or Lagrangian averaged Navier-Stokes equations) with fractional diffusion in both smooth bounded domains and in the whole space in two and three dimensions. Order of the…
In \cite{CJ}, the authors show that the Cauchy problem of the Navier-Stokes equations with damping $\alpha|u|^{\beta-1}u(\alpha>0,\;\beta\geq1)$ has global weak solutions in $L^2(\R^3)$. In this paper, we prove the uniqueness, the…
Chemical and biochemical reactions can exhibit surprisingly different behaviours, ranging from multiple steady-state solutions to oscillatory solutions and chaotic behaviours. These types of systems are often modelled by a system of…
In this work we investigate the existence of weak solutions for steady flows of generalized incompressible and homogeneous viscous fluids. The problem is modeled by the steady case of the generalized Navier-Stokes equations, where the…
This paper deals with the following quasilinear Keller-Segel-Navier-Stokes system modeling coral fertilization $(*)$: $$\left\{ \begin{array}{l} n_t+u\cdot\nabla n=\Delta n-\nabla\cdot(nS(x,n,c)\nabla c)-nm,\quad x\in \Omega, t>0,…
We consider a parabolic-elliptic type of Keller-Segel equations with generalized diffusion and logistic source under homogeneous Neumann-Neumann boundary conditions. We construct bounded weak solutions globally in time in an unbalanced…
By applying Wiegner' method in \cite{Wiegner}, we first prove the large time decay estimate for the global solutions of a 2.5 dimensional Navier-Stokes system, which is a sort of singular perturbed 2-D Navier-Stokes system in three space…
New estimates and global existence results are provided for a class of systems of cross diffusion equations arising from the modeling of chemotaxis with local sensing, possibly featuring a growth term of logistic-type as well. For sublinear…
In this paper we obtain the existence of global attractors for the dynamical systems generated by weak solution of the three-dimensional Navier-Stokes equations with damping. We consider two cases, depending on the values of the parameters…
The friction-type interface condition (FIC) is introduced to describe the phenomenon of the slip and leak of fluid flow on the interface happens only when the difference of stress force is above a threshold. The FIC involves the…
We consider a chemotaxis-fluid system involving nonlinear cell diffusion of porous medium type, signal consumption by cells, and rather general, possibly matrix-valued, chemotactic sensitivities. It is shown that if the corresponding…
For periodic initial data with the density allowing vacuum, we establish the global existence and exponential decay of weak, strong and classical solutions to the two-dimensional(2D) compressible Navier-Stokes equations when the bulk…