Localized minimizers of flat rotating gravitational systems
Locally periodic homogenization of reflected diffusion.
Locating the boundary peaks of least-energy solutions to a singularly perturbed Dirichlet problem
We consider the problemwhere is a smooth and bounded domain,
Location of resonances generated by degenerate potential barrier.
Logarithmic decay of the energy for an hyperbolic-parabolic coupled system
This paper is devoted to the study of a coupled system which consists of a wave equation and a heat equation coupled through a transmission condition along a steady interface. This system is a linearized model for fluid-structure interaction introduced by Rauch, Zhang and Zuazua for a simple transmission condition and by Zhang and Zuazua for a natural transmission condition. Using an abstract theorem of Burq and a new Carleman estimate proved near the interface, we complete the results obtained...
Logarithmic decay of the energy for an hyperbolic-parabolic coupled system
This paper is devoted to the study of a coupled system which consists of a wave equation and a heat equation coupled through a transmission condition along a steady interface. This system is a linearized model for fluid-structure interaction introduced by Rauch, Zhang and Zuazua for a simple transmission condition and by Zhang and Zuazua for a natural transmission condition. Using an abstract theorem of Burq and a new Carleman estimate proved near the interface, we complete the results obtained...
Logarithmically improved blow-up criterion for smooth solutions to the Leray--magnetohydrodynamic equations
In this paper, the Cauchy problem for the Leray--MHD model is investigated. We obtain the logarithmically improved blow-up criterion of smooth solutions for the Leray--MHD model in terms of the magnetic field only in the framework of homogeneous Besov space with negative index.
Logarithmically improved regularity criteria for the micropolar fluid equations
We discuss the 3D incompressible micropolar fluid equations, and give logarithmically improved regularity criteria in terms of both the velocity field and the pressure in Morrey-Campanato spaces, BMO spaces and Besov spaces.
Log-concavity in some parabolic problems.
Lokale Abschätzungen und Randverhalten von Lösungen elliptischer Monge-Ampèrescher Gleichungen.
Lokale Kerne und beschränkte Lösungen für den ...-Operator auf q-konvexen Gebieten.
Long time asymptotics of the Camassa–Holm equation on the half-line
We study the long-time behavior of solutions of the initial-boundary value (IBV) problem for the Camassa–Holm (CH) equation on the half-line . The paper continues our study of IBV problems for the CH equation, the key tool of which is the formulation and analysis of associated Riemann–Hilbert factorization problems. We specify the regions in the quarter space-time plane , having qualitatively different asymptotic pictures, and give the main terms of the asymptotics in terms of spectral data...
Long time averaged reflection force and homogenization of oscillating Neumann boundary conditions
Long time behaviour of a Cahn-Hilliard system coupled with viscoelasticity
The long-time behaviour of a unique regular solution to the Cahn-Hilliard system coupled with viscoelasticity is studied. The system arises as a model of the phase separation process in a binary deformable alloy. It is proved that for a sufficiently regular initial data the trajectory of the solution converges to the ω-limit set of these data. Moreover, it is shown that every element of the ω-limit set is a solution of the corresponding stationary problem.
Long time dynamics for the one dimensional non linear Schrödinger equation
In this article, we first present the construction of Gibbs measures associated to nonlinear Schrödinger equations with harmonic potential. Then we show that the corresponding Cauchy problem is globally well-posed for rough initial conditions in a statistical set (the support of the measures). Finally, we prove that the Gibbs measures are indeed invariant by the flow of the equation. As a byproduct of our analysis, we give a global well-posedness and scattering result for the critical and super-critical...
Long time estimate of solutions to 3d Navier-Stokes equations coupled with heat convection
We examine the Navier-Stokes equations with homogeneous slip boundary conditions coupled with the heat equation with homogeneous Neumann conditions in a bounded domain in ℝ³. The domain is a cylinder along the x₃ axis. The aim of this paper is to show long time estimates without assuming smallness of the initial velocity, the initial temperature and the external force. To prove the estimate we need however smallness of the L₂ norms of the x₃-derivatives of these three quantities.
Long time existence of regular solutions to 3d Navier-Stokes equations coupled with heat convection
We prove long time existence of regular solutions to the Navier-Stokes equations coupled with the heat equation. We consider the system in a non-axially symmetric cylinder, with the slip boundary conditions for the Navier-Stokes equations, and the Neumann condition for the heat equation. The long time existence is possible because the derivatives, with respect to the variable along the axis of the cylinder, of the initial velocity, initial temperature and external force are assumed to be sufficiently...
Long-Range and Periodic Solutions of Parabolic Problems.
Long-term damped dynamics of the extensible suspension bridge.
Long-time asymptotics for the damped Boussinesq equation in a disk.