On the Semigroup of the Stokes Operator for Exterior Domains in Lq-Spaces.
On the Singular Set and the Uniqueness of Weak Solutions of the Navier-Stokes Equations.
On the small time asymptotics of the two-dimensional stochastic Navier–Stokes equations
In this paper, we establish a small time large deviation principle (small time asymptotics) for the two-dimensional stochastic Navier–Stokes equations driven by multiplicative noise, which not only involves the study of the small noise, but also the investigation of the effect of the small, but highly nonlinear, unbounded drifts.
On the smallness of the (possible) singular set in space for 3D Navier-Stokes equations.
On the solution of transonic flows with weak shocks
On the stationary motion of a Stokes fluid in a thick elastic tube: a 3D/3D interaction problem.
On the steady translational self-propelled motion of a body in a Navier-Stokes fluid
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 strong solution for the 3D stochastic Leray- model.
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 two-dimensional compressible isentropic Navier–Stokes equations
We analyze the compressible isentropic Navier–Stokes equations (Lions, 1998) in the two-dimensional case with . These equations also modelize the shallow water problem in height-flow rate formulation used to solve the flow in lakes and perfectly well-mixed sea. We establish a convergence result for the time-discretized problem when the momentum equation and the continuity equation are solved with the Galerkin method, without adding a penalization term in the continuity equation as it is made in...
On the two-dimensional compressible isentropic Navier–Stokes equations
We analyze the compressible isentropic Navier–Stokes equations (Lions, 1998) in the two-dimensional case with . These equations also modelize the shallow water problem in height-flow rate formulation used to solve the flow in lakes and perfectly well-mixed sea. We establish a convergence result for the time-discretized problem when the momentum equation and the continuity equation are solved with the Galerkin method, without adding a penalization term in the continuity equation as it is made in Lions...
On the uniqueness of bounded weak solutions to the Navier-Stokes Cauchy problem
On the uniqueness of weak solutions for the 3D Navier-Stokes equations
On the asymptotic properties of solutions of the Navier-Stokes equations in the half-space.
On variational inequalities associated with the Navier-Stokes equation: Some bifurcation problems.
On various types of viscous two-fluid flows
Viscous two-fluid flows arise in different kinds of coating technologies. Frequently, the corresponding mathematical models represent two-dimensional free boundary value problems for the Navier-Stokes equations or their modifications. In this review article we present some results about nonisothermal stationary as well as about isothermal evolutionary viscous flow problems. The temperature-depending problems are characterized by coupled heat- and mass transfer and also by thermocapillary convection....
On weak solutions of steady Navier-Stokes equations for monatomic gas
We use estimates for the inverse Laplacian of the pressure introduced by Plotnikov, Sokolowski and Frehse, Goj, Steinhauer together with the nonlinear potential theory due to Adams, Hedberg, to get a priori estimates and to prove existence of weak solutions to steady isentropic Navier-Stokes equations with the adiabatic constant for the flows powered by volume non-potential forces and with for the flows powered by potential forces and arbitrary non-volume forces. According to our knowledge,...