On the Regularity Conditions for the Navier-Stokes and Related Equations.
On the regularity for solutions of the micropolar fluid equations
On the regularity of the bilinear term for solutions to the incompressible Navier-Stokes equations.
We derive various estimates for strong solutions to the Navier-Stokes equations in C([0,T),L3(R3)) that allow us to prove some regularity results on the kinematic bilinear term.
On the regularity of the stationary Navier-Stokes equations
On the result of He concerning the smoothness of solutions to the Navier-Stokes equations.
On the search for singularities in incompressible flows
In these notes we give some examples of the interaction of mathematics with experiments and numerical simulations on the search for singularities.
On the second order slip Reynolds equation with molecular dynamics: existence and uniqueness.
On the Semigroup of the Stokes Operator for Exterior Domains in Lq-Spaces.
On the smallness of the (possible) singular set in space for 3D Navier-Stokes equations.
On the Stability of Bilinear-Constant Velocity-Pressure Finite Elements.
On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations
We consider the coupling between three-dimensional (3D) and one-dimensional (1D) fluid-structure interaction (FSI) models describing blood flow inside compliant vessels. The 1D model is a hyperbolic system of partial differential equations. The 3D model consists of the Navier-Stokes equations for incompressible Newtonian fluids coupled with a model for the vessel wall dynamics. A non standard formulation for the Navier-Stokes equations is adopted to have suitable boundary conditions for the...
On the stationary motion of granulated media
On the Stokes and Navier-Stokes flows in a perturbed half-space
We give the estimate for the Stokes semigroup in a perturbed half-space and some global in time existence theorems for small solutions to the Navier-Stokes equation.
On the Stokes equation with Neumann boundary condition
In this paper, we study the nonstationary Stokes equation with Neumann boundary condition in a bounded or an exterior domain in ℝⁿ, which is the linearized model problem of the free boundary value problem. Mainly, we prove estimates for the semigroup of the Stokes operator. Comparing with the non-slip boundary condition case, we have the better decay estimate for the gradient of the semigroup in the exterior domain case because of the null force at the boundary.
On the structure of flows through pipe-like domains satisfying a geometrical constraint
We study solutions of the steady Navier-Stokes equations in a bounded 2D domain with the slip boundary conditions admitting flow across the boundary. We show conditions guaranteeing uniqueness of the solution. Next, we examine the structure of the solution considering an approximation given by a natural linearization. Suitable error estimates are also obtained.
On the Transport-Diffusion Algorithm and Its Applications to the NavierStokes Equations.
On the uniqueness of solutions in the class of increasing functions of a system describing the dynamics of a viscous weakly stratified fluid in three-dimensional space.
On the asymptotic properties of solutions of the Navier-Stokes equations in the half-space.
On Unsteady Boundary Layers In A Rotating Fluid With Time-Dependent Suction
On unsteady three-dimensional boundary layer.