On the global stability of contact discontinuity for compressible Navier-Stokes equations
On the global wellposedness of the 3-D Navier–Stokes equations with large initial data
On the inf-sup condition for higher order mixed FEM on meshes with hanging nodes
We consider higher order mixed finite element methods for the incompressible Stokes or Navier-Stokes equations with Qr-elements for the velocity and discontinuous -elements for the pressure where the order r can vary from element to element between 2 and a fixed bound . We prove the inf-sup condition uniformly with respect to the meshwidth h on general quadrilateral and hexahedral meshes with hanging nodes.
On the instantaneous spreading for the Navier–Stokes system in the whole space
We consider the spatial behavior of the velocity field of a fluid filling the whole space () for arbitrarily small values of the time variable. We improve previous results on the spatial spreading by deducing the necessary conditions under more general assumptions on the localization of . We also give some new examples of solutions which have a stronger spatial localization than in the generic case.
On the Instantaneous Spreading for the Navier–Stokes System in the Whole Space
We consider the spatial behavior of the velocity field u(x, t) of a fluid filling the whole space () for arbitrarily small values of the time variable. We improve previous results on the spatial spreading by deducing the necessary conditions under more general assumptions on the localization of u. We also give some new examples of solutions which have a stronger spatial localization than in the generic case.
On the integral representation of the solution to the Stokes system
On the interior regularity of weak solutions of non-stationary Navier-Stokes equations on a riemannian manifold
On the Ladyzhenskaya-Smagorinsky turbulence model of the Navier-Stokes equations in smooth domains. The regularity problem
We establish regularity results up to the boundary for solutions to generalized Stokes and Navier–Stokes systems of equations in the stationary and evolutive cases. Generalized here means the presence of a shear dependent viscosity. We treat the case . Actually, we are interested in proving regularity results in spaces for all the second order derivatives of the velocity and all the first order derivatives of the pressure. The main aim of the present paper is to extend our previous scheme, introduced...
On the local strong solutions for a system describing the flow of a viscoelastic fluid
We consider a model for the viscoelastic fluid which has recently been studied in [4] and [1]. We show the local-in-time existence of a strong solution to the corresponding system of partial differential equations under less regularity assumptions on the initial data than in the above mentioned papers. The main difference in our approach is the use of the theory for the Stokes system.
On the long-time behaviour of compressible fluid flows subjected to highly oscillating external forces
We show that the global-in-time solutions to the compressible Navier-Stokes equations driven by highly oscillating external forces stabilize to globally defined (on the whole real line) solutions of the same system with the driving force given by the integral mean of oscillations. Several stability results will be obtained.
On the maximum modulus theorem for the Stokes system
On the motion of rigid bodies in a viscous fluid
We consider the problem of motion of several rigid bodies in a viscous fluid. Both compressible and incompressible fluids are studied. In both cases, the existence of globally defined weak solutions is established regardless possible collisions of two or more rigid objects.
On the Navier-Stokes Equations in Non-Cylindrical Domains: On the Existence and Regularity.
On the Navier-Stokes equations with temperature-dependent transport coefficients.
On the parameter in augmented Lagrangian preconditioning for isogeometric discretizations of the Navier-Stokes equations
In this paper, we deal with the optimal choice of the parameter for augmented Lagrangian preconditioning of GMRES method for efficient solution of linear systems obtained from discretization of the incompressible Navier-Stokes equations. We consider discretization of the equations using the B-spline based isogeometric analysis approach. We are interested in the dependence of the convergence on the parameter for various problem parameters (Reynolds number, mesh refinement) and especially for...
On the regular solutions for some classes of Navier-Stokes equations
On the Regularity Conditions for the Navier-Stokes and Related 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.