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Error of the two-step BDF for the incompressible Navier-Stokes problem

Etienne Emmrich (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The incompressible Navier-Stokes problem is discretized in time by the two-step backward differentiation formula. Error estimates are proved under feasible assumptions on the regularity of the exact solution avoiding hardly fulfillable compatibility conditions. Whereas the time-weighted velocity error is of optimal second order, the time-weighted error in the pressure is of first order. Suboptimal estimates are shown for a linearisation. The results cover both the two- and three-dimensional...

Essential m-dissipativity of Kolmogorov operators corresponding to periodic 2 ⁢ D -Navier Stokes equations

Viorel Barbu, Giuseppe Da Prato, Arnaud Debussche (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We prove the essential m-dissipativity of the Kolmogorov operator associated with the stochastic Navier-Stokes flow with periodic boundary conditions in a space L 2 ⁢ H , ν where ν is an invariant measure

Estimate of the pressure when its gradient is the divergence of a measure. Applications

Marc Briane, Juan Casado-Díaz (2011)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, a W - 1 , N ' estimate of the pressure is derived when its gradient is the divergence of a matrix-valued measure on ℝ N , or on a regular bounded open set of  ℝ N . The proof is based partially on the Strauss inequality [Strauss,Partial Differential Equations: Proc. Symp. Pure Math. 23 (1973) 207–214] in dimension two, and on a recent result of Bourgain and Brezis [J. Eur. Math. Soc. 9 (2007) 277–315] in higher dimension. The estimate is used to derive a representation result for divergence free distributions...

Estimate of the pressure when its gradient is the divergence of a measure. Applications

Marc Briane, Juan Casado-Díaz (2011)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, a W - 1 , N ' estimate of the pressure is derived when its gradient is the divergence of a matrix-valued measure on ℝ N , or on a regular bounded open set of  ℝ N . The proof is based partially on the Strauss inequality [Strauss, Partial Differential Equations: Proc. Symp. Pure Math.23 (1973) 207–214] in dimension two, and on a recent result of Bourgain and Brezis [J. Eur. Math. Soc.9 (2007) 277–315] in higher dimension. The estimate is used to derive a representation result for divergence free distributions...

Estimates of lower order derivatives of viscous fluid flow past a rotating obstacle

Reinhard Farwig (2005)

Banach Center Publications

Consider the problem of time-periodic strong solutions of the Stokes system modelling viscous incompressible fluid flow past a rotating obstacle in the whole space ℝ³. Introducing a rotating coordinate system attached to the body yields a system of partial differential equations of second order involving an angular derivative not subordinate to the Laplacian. In a recent paper [2] the author proved L q -estimates of second order derivatives uniformly in the angular and translational velocities, ω and...

Exact boundary controllability of 3-D Euler equation

Olivier Glass (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We prove the exact boundary controllability of the 3-D Euler equation of incompressible inviscid fluids on a regular connected bounded open set when the control operates on an open part of the boundary that meets any of the connected components of the boundary.

Existence and uniqueness results for non-Newtonian fluids of the Oldroyd type in unbounded domains

Rodolfo Salvi (2005)

Banach Center Publications

In the paper [13], we give the full system of equations modelling the motion of a fluid/viscoelastic solid system, and obtain a differential model similar to the so-called Oldroyd model for a viscoelastic fluid. Moreover, existence results in bounded domains are obtained. In this paper we extend the results in [13] to unbounded domains. The unique solvability of the system of equations is established locally in time and globally in time with so-called smallness restrictions. Moreover, existence...

Existence for an Unsteady Fluid-Structure Interaction Problem

Céline Grandmont, Yvon Maday (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We study the well-posedness of an unsteady fluid-structure interaction problem. We consider a viscous incompressible flow, which is modelled by the Navier-Stokes equations. The structure is a collection of rigid moving bodies. The fluid domain depends on time and is defined by the position of the structure, itself resulting from a stress distribution coming from the fluid. The problem is then nonlinear and the equations we deal with are coupled. We prove its local solvability in time through two...

Existence for the stationary MHD-equations coupled to heat transfer with nonlocal radiation effects

Pierre-Étienne Druet (2009)

Czechoslovak Mathematical Journal

We consider the problem of influencing the motion of an electrically conducting fluid with an applied steady magnetic field. Since the flow is originating from buoyancy, heat transfer has to be included in the model. The stationary system of magnetohydrodynamics is considered, and an approximation of Boussinesq type is used to describe the buoyancy. The heat sources given by the dissipation of current and the viscous friction are not neglected in the fluid. The vessel containing the fluid is embedded...

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