Réduction de la résolution d'un problème de réseau maillé (B) : sur la convergence locale de certaines méthodes
Reduction of boundary value problem to Possio integral equation in theoretical aeroelasticity.
Reductions in a class of dissipative dynamical systems of macroscopic physics
Reflection and dissipation of oblique Alfvén waves in an isothermal atmosphere.
Reflection on internal waves by sand ripples.
Regular solutions of the Navier-Stokes system.
Regular solutions of the stationary Navier-Stokes equations on ....
Régularité du problème de Kelvin–Helmholtz pour l’équation d’Euler 2D
Nous prouvons que pour toute solution du problème de Kelvin–Helmholtz des nappes de tourbillons pour l’équation d’Euler bi-dimensionnelle, définie localement en temps, la courbe de saut de et la densité de tourbillon sont analytiques (sous une hypothèse de régularité Holderienne de la courbe de saut). Nous donnons également un résultat de régularité partielle de la trace de sur lorsque est définie sur un demi-interval .
Régularité du problème de Kelvin-Helmholtz pour l’équation d’Euler 2d
Régularité du problème de Kelvin–Helmholtz pour l'équation d'Euler 2d
Nous prouvons que pour toute solution u du problème de Kelvin–Helmholtz des nappes de tourbillons pour l'équation d'Euler bi-dimensionnelle, définie localement en temps, la courbe de saut de u et la densité de tourbillon sont analytiques (sous une hypothèse de régularité Holderienne de la courbe de saut). Nous donnons également un résultat de régularité partielle de la trace de u sur t=0 lorsque u est définie sur un demi-interval [O,T[.
Regularity and Blow up for Active Scalars
We review some recent results for a class of fluid mechanics equations called active scalars, with fractional dissipation. Our main examples are the surface quasi-geostrophic equation, the Burgers equation, and the Cordoba-Cordoba-Fontelos model. We discuss nonlocal maximum principle methods which allow to prove existence of global regular solutions for the critical dissipation. We also recall what is known about the possibility of finite time blow...
Regularity and decay of 3D incompressible MHD equations with nonlinear damping terms
We prove the existence and uniqueness of global strong solutions to the Cauchy problem for 3D incompressible MHD equations with nonlinear damping terms. Moreover, the preliminary L² decay for weak solutions is also established.
Regularity and stability of optimal controls of nonstationary Navier-Stokes equations
Regularity and uniqueness for the stationary large eddy simulation model
In the note we are concerned with higher regularity and uniqueness of solutions to the stationary problem arising from the large eddy simulation of turbulent flows. The system of equations contains a nonlocal nonlinear term, which prevents straightforward application of a difference quotients method. The existence of weak solutions was shown in A. Świerczewska: Large eddy simulation. Existence of stationary solutions to the dynamical model, ZAMM, Z. Angew. Math. Mech. 85 (2005), 593–604 and P....
Regularity criterion for 3D Navier-Stokes equations in terms of the direction of the velocity
In this short note we give a link between the regularity of the solution to the 3D Navier-Stokes equation and the behavior of the direction of the velocity . It is shown that the control of in a suitable norm is enough to ensure global regularity. The result is reminiscent of the criterion in terms of the direction of the vorticity, introduced first by Constantin and Fefferman. However, in this case the condition is not on the vorticity but on the velocity itself. The proof, based on very...
Regularity criterion for a nonhomogeneous incompressible Ginzburg-Landau-Navier-Stokes system
We prove a regularity criterion for a nonhomogeneous incompressible Ginzburg-Landau-Navier-Stokes system with the Coulomb gauge in . It is proved that if the velocity field in the Besov space satisfies some integral property, then the solution keeps its smoothness.
Regularity criterion for weak solutions to the Navier-Stokes equations in terms of the gradient of the pressure.
Regularity for 3D Navier-Stokes equations in terms of two components of the vorticity.
Regularity for doubly nonlinear parabolic equations
Regularity for solutions to the Navier-Stokes equations with one velocity component regular.