Global well-posedness for the 2-D Boussinesq system with temperature-dependent thermal diffusivity
We prove the global well-posedness of the 2-D Boussinesq system with temperature dependent thermal diffusivity and zero viscosity coefficient.
Global well-posedness for the 2D quasi-geostrophic equation in a critical Besov space.
Global well-posedness for the Klein-Gordon-Schrödinger system with higher order coupling
Global well-posedness for the Klein-Gordon-Schrödinger system with generalized higher order coupling, which is a system of PDEs in two variables arising from quantum physics, is proven. It is shown that the system is globally well-posed in under some conditions on the nonlinearity (the coupling term), by using the conservation law for and controlling the growth of via the estimates in the local theory. In particular, this extends the well-posedness results for such a system in Miao, Xu (2007)...
Global well-posedness for the primitive equations with less regular initial data
This paper is devoted to the study of the lifespan of the solutions of the primitive equations for less regular initial data. We interpolate the globall well-posedness results for small initial data in given by the Fujita-Kato theorem, and the result from [6] which gives global well-posedness if the Rossby parameter is small enough, and for regular initial data (oscillating part in and quasigeostrophic part in ).
Global well-posedness for the radial defocusing cubic wave equation on and for rough data.
Global well-posedness for two-dimensional semilinear wave equations.
Global well-posedness of NLS-KdV systems for periodic functions.
Global well-posedness of the Cauchy problem of a higher-order Schrödinger equation.
Global well-posedness of the initial value problem for the Hirota-Satsuma system.
Global well-posedness, scattering and blow-up for the energy-critical, focusing Hartree equation in the radial case
We establish global existence and scattering for radial solutions to the energy-critical focusing Hartree equation with energy and Ḣ¹ norm less than those of the ground state in , d ≥ 5.
Global φ-attractor for a modified 3D Bénard system on channel-like domains
In this paper we prove the existence of a global φ-attractor in the weak topology of the natural phase space for the family of multi-valued processes generated by solutions of a nonautonomous modified 3D Bénard system in unbounded domains for which Poincaré inequality takes place.
Globalization of SQP-methods in control of the instationary Navier-Stokes equations
A numerically inexpensive globalization strategy of sequential quadratic programming methods (SQP-methods) for control of the instationary Navier Stokes equations is investigated. Based on the proper functional analytic setting a convergence analysis for the globalized method is given. It is argued that the a priori formidable SQP-step can be decomposed into linear primal and linear adjoint systems, which is amenable for existing CFL-software. A report on a numerical test demonstrates the feasibility...
Globalization of SQP-Methods in Control of the Instationary Navier-Stokes Equations
A numerically inexpensive globalization strategy of sequential quadratic programming methods (SQP-methods) for control of the instationary Navier Stokes equations is investigated. Based on the proper functional analytic setting a convergence analysis for the globalized method is given. It is argued that the a priori formidable SQP-step can be decomposed into linear primal and linear adjoint systems, which is amenable for existing CFL-software. A report on a numerical test demonstrates the feasibility...
Global-Local subadditive ergodic theorems and application to homogenization in elasticity
Globally regular solutions to the Klein-Gordon equation
Gluing approximate solutions of minimum type on the Nehari manifold.
Godunov method for nonconservative hyperbolic systems
This paper is concerned with the numerical approximation of Cauchy problems for one-dimensional nonconservative hyperbolic systems. The theory developed by Dal Maso et al. [J. Math. Pures Appl.74 (1995) 483–548] is used in order to define the weak solutions of the system: an interpretation of the nonconservative products as Borel measures is given, based on the choice of a family of paths drawn in the phase space. Even if the family of paths can be chosen arbitrarily, it is natural to require this...
Goursat and Darboux type problems for linear hyperbolic partial differential equations and systems.
Gradient alternating-direction methods
Gradient bounds and Liouville theorems for quasilinear elliptic equations