Editorial comment on the paper Huashui Zhan, Junning Zhao: Some remarks on Prandtl system
Effects of Hall current on the pulsating flow of a third grade fluid.
Effects of magnetic field and nonlinear temperature profile on Marangoni convection in micropolar fluid.
Ekman boundary layers in rotating fluids
In this paper, we investigate the problem of fast rotating fluids between two infinite plates with Dirichlet boundary conditions and “turbulent viscosity” for general initial data. We use dispersive effect to prove strong convergence to the solution of the bimensionnal Navier-Stokes equations modified by the Ekman pumping term.
Ekman boundary layers in rotating fluids
In this paper, we investigate the problem of fast rotating fluids between two infinite plates with Dirichlet boundary conditions and “turbulent viscosity” for general L2 initial data. We use dispersive effect to prove strong convergence to the solution of the bimensionnal Navier-Stokes equations modified by the Ekman pumping term.
Entropy solutions to the Buckley--Leverett equations.
Equivalence transformations of the Clebsch equations.
Estimate of the pressure when its gradient is the divergence of a measure. Applications
In this paper, a estimate of the pressure is derived when its gradient is the divergence of a matrix-valued measure on , or on a regular bounded open set of . 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
In this paper, a estimate of the pressure is derived when its gradient is the divergence of a matrix-valued measure on , or on a regular bounded open set of . 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 based on scale separation for geophysical flows.
The objective of this work is to obtain theoretical estimates on the large and small scales for geophysical flows. Firstly, we consider the shallow water problem in the one-dimensional case, then in the two-dimensional case. Finally we consider geophysical flows under the hydrostatic hypothesis and the Boussinesq approximation. Scale separation is based on Fourier series, with N models in each spatial direction, and the choice of a cut-off level N1 < N to define large and small scales. We...
Estimates for the maximum modulus of solutions to the Burgers system of equations.
Estimates in Besov spaces for transport and transport-diffusion equations with almost Lipschitz coefficients.
This paper aims at giving an overview of estimates in general Besov spaces for the Cauchy problem on t = 0 related to the vector field ∂t + v·∇. The emphasis is on the conservation or loss of regularity for the initial data.When ∇u belongs to L1(0,T; L∞) (plus some convenient conditions depending on the functional space considered for the data), the initial regularity is preserved. On the other hand, if ∇v is slightly less regular (e.g. ∇v belogs to some limit space for which the embedding in L∞...
Euler and Navier-Stokes equations.
Evolution by the vortex filament equation of curves with a corner
In this proceedings article we shall survey a series of results on the stability of self-similar solutions of the vortex filament equation. This equation is a geometric flow for curves in and it is used as a model for the evolution of a vortex filament in fluid mechanics. The main theorem give, under suitable assumptions, the existence and description of solutions generated by curves with a corner, for positive and negative times. Its companion theorem describes the evolution of perturbations...
Évolution de tourbillon à support compact
On considère l’équation d’Euler incompressible dans le plan. Dans le cas où le tourbillon est positif et à support compact on montre que le support du tourbillon croît au plus comme , améliorant la borne obtenue par C. Marchioro. Dans le cas où le tourbillon change de signe, on donne un exemple de tourbillon initial tel que la croissance du diamètre du support du tourbillon est exactement . Enfin, dans le cas du demi-plan et du tourbillon initial positif et à support compact, on montre que le...
Évolution d'une singularité de type cusp dans une poche de tourbillon
Évolution d'une singularité de type cusp dans une poche de tourbillon.
We investigate the evolution of singularities in the boundary of a vortex patch for two-dimensional incompressible Euler equations. We are particularly interested in cusp-like singularities which, according to numerical simulations, are stable. In this paper, we first prove that, unlike the case of a corner-like singularity, the cusp-like singularity generates a lipschitzian velocity. We then state a global result of persistence of conormal regularity with respect to vector fields vanishing at a...
Exact boundary controllability of 3-D Euler equation
Exact boundary controllability of 3-D Euler equation
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.
Exact solutions of steady plane flows using -coordinates.