Global weak solutions of the Navier-Stokes equations with nonhomogeneous boundary data and divergence
Global weak solvability of a regularized system of the Navier-Stokes equations for compressible fluid
The paper contains the proof of global existence of weak solutions to the mixed initial-boundary value problem for a certain modification of a system of equations of motion of viscous compressible fluid. The modification is based on an application of an operator of regularization to some terms appearing in the system of equations and it does not contradict the laws of fluid mechanics. It is assumed that pressure is a known function of density. The method of discretization in time is used and finally,...
Global weak solvability to the regularized viscous compressible heat conductive flow
The concept of regularization to the complete system of Navier-Stokes equations for viscous compressible heat conductive fluid is developed. The existence of weak solutions for the initial boundary value problem for the modified equations is proved. Some energy and etropy estimates independent of the parameter of regularization are derived.
Global well-posedness and blow up for the nonlinear fractional beam equations
We establish the Strichartz estimates for the linear fractional beam equations in Besov spaces. Using these estimates, we obtain global well-posedness for the subcritical and critical defocusing fractional beam equations. Of course, we need to assume small initial data for the critical case. In addition, by the convexity method, we show that blow up occurs for the focusing fractional beam equations with negative energy.
Global well-posedness and scattering for the defocusing -subcritical Hartree equation in
Global well-posedness and scattering for the derivative nonlinear Schrödinger equation with small rough data
Global well-posedness and scattering for the higher-dimensional energy-critical nonlinear Schrödinger equation for radial data.
Global well-posedness for KdV in Sobolev spaces of negative index.
Global well-posedness for Schrödinger equations with derivative in a nonlinear term and data in low-order Sobolev spaces.
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 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...