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 $(u,n)\in L^2\times L^2$ under some conditions on the nonlinearity (the coupling term), by using the $L^2$ conservation law for $u$ and controlling the growth of $n$ via the estimates in the local theory. In particular, this extends the well-posedness results for such a system in Miao, Xu (2007)...

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 ${\dot{H}}^{\frac{1}{2}}$ given by the Fujita-Kato theorem, and the result from [6] which gives global well-posedness if the Rossby parameter $\epsilon$ is small enough, and for regular initial data (oscillating part in ${\dot{H}}^{\frac{1}{2}}\cap {\dot{H}}^1$ and quasigeostrophic part in $H^1$).

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 $ℝ\times {ℝ}^d$, d ≥ 5.

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.

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...

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...

The paper presents the solution to the geodetic boundary value problem by the finite element method in area of Slovak Republic. Generally, we have made two numerical experiments. In the first one, Neumann BC in the form of gravity disturbances generated from EGM-96 is used and the solution is verified by the quasigeoidal heights generated directly from EGM-96. In the second one, Neumann BC is computed from gravity measurements and the solution is compared to the quasigeoidal heights obtained by...

The aim of this paper is to find estimates of the Green’s function of stationary discrete shock profiles and discrete boundary layers of the modified Lax–Friedrichs numerical scheme, by using techniques developed by Zumbrun and Howard [27] in the continuous viscous setting.

The aim of this paper is to find estimates of the Green's function of stationary discrete shock profiles and discrete boundary layers of the modified Lax–Friedrichs numerical scheme, by using techniques developed by Zumbrun and Howard [CITE] in the continuous viscous setting.

In this preliminary Note we outline the results of the forthcoming paper [2] dealing with a class on nonlinear Schrödinger equations with potentials vanishing at infinity. Working in weighted Sobolev spaces, the existence of a ground state is proved. Furthermore, the behaviour of such a solution, as the Planck constant tends to zero (semiclassical limit), is studied proving that it concentrates at a point.

We deal with a class on nonlinear Schrödinger equations (NLS) with potentials $V\left(x\right)\sim {\left|x\right|}^{-\alpha }$, $0<\alpha <2$, and $K\left(x\right)\sim {\left|x\right|}^{-\beta }$, $\beta >0$. Working in weighted Sobolev spaces, the existence of ground states $v_{\epsilon }$ belonging to $W^{1,2}\left({ℝ}^N\right)$ is proved under the assumption that $\sigma <p<(N+2)/\left(N-2\right)$ for some $\sigma ={\sigma }_{N,\alpha ,\beta }$. Furthermore, it is shown that $v_{\epsilon }$ are spikes concentrating at a minimum point of $𝒜=V^{\theta }{K}^{-2/\left(p-1\right)}$, where $\theta =(p+1)/\left(p-1\right)-1/2$.

This text aims to describe results of the authors on the long time behavior of NLS on product spaces with a particular emphasis on the existence of solutions with growing higher Sobolev norms.