System In Critical Spaces Research Articles

THE GLOBAL STRONG SOLUTIONS OF THE 3D INCOMPRESSIBLE HALL-MHD SYSTEM WITH VARIABLE DENSITY

In this paper, we focus on the well-posedness problem of the three-dimensional incompressible viscous and resistive Hall-magnetohydrodynamics system (Hall-MHD) with variable density. We mainly prove the existence and uniqueness issues of the density-dependent incompressible Hall-magnetohydrodynamic system in critical spaces on R3.

Well-posedness for the Boussinesq system in critical spaces via maximal regularity

We establish the existence and the uniqueness for the Boussinesq system in the whole 3D space in the critical space of continuous in time with values in the power 3 integrable in space functions for the velocity and square integrable in time with values in the power 3/2 integrable in space.

Global well-posedness and decay estimate for the 2-D Boussinesq system in critical spaces

Global well-posedness and decay estimate for the 2-D Boussinesq system in critical spaces

The combined quasineutral and incompressible limit for the Navier–Stokes–Poisson system in critical spaces

In this paper, we study the quasineutral and incompressible limit for the Navier–Stokes–Poisson system with ill-prepared initial data in whole space. Based on Strichartz estimates for the Klein–Gordon equation and the pseudo-scaling property of modified Besov norms, we prove that the density tends to a constant, the compressible part of velocity vanishes, and the incompressible part of velocity converges to the solution of the incompressible Navier–Stokes equation. We get a relation of the lifespan of the solution between the Navier–Stokes–Poisson and the incompressible Navier–Stokes equations for small Debye length and low Mach number.

On the well-posedness of the Hall-magnetohydrodynamics system in critical spaces

We investigate the existence and uniqueness issues of the 3D incompressible Hall-magnetohydrodynamic system supplemented with initial velocity u0 and magnetic field B0 in critical regularity spaces. In the case where u0, B0 and the current belong to the homogeneous Besov space and are small enough, we establish a global result and the conservation of higher regularity. If the viscosity is equal to the magnetic resistivity, then we obtain the global well-posedness provided u0, B0 and J0 are small enough in the larger Besov space If then we also establish the local existence for large data, and exhibit continuation criteria for solutions with critical regularity. Our results rely on an extended formulation of the Hall-MHD system that has some similarities with the incompressible Navier–Stokes equations.

Temporal decay of a global solution to 3D magnetohydrodynamic system in critical spaces

Temporal decay of a global solution to 3D magnetohydrodynamic system in critical spaces

On the Majorana condition for nonlinear Dirac systems

For arbitrarily large initial data in an open set defined by an approximate Majorana condition, global existence and scattering results for solutions to the Dirac equation with Soler-type nonlinearity and the Dirac–Klein–Gordon system in critical spaces in spatial dimension three are established.

CONDITIONAL LARGE INITIAL DATA SCATTERING RESULTS FOR THE DIRAC–KLEIN–GORDON SYSTEM

We consider the global behaviour for large solutions of the Dirac–Klein–Gordon system in critical spaces in dimension$1+3$. In particular, we show that bounded solutions exist globally in time and scatter, provided that a controlling space–time Lebesgue norm is finite. A crucial step is to prove nonlinear estimates that exploit the dichotomy between transversality and null structure, and furthermore involve the controlling norm.

Local Well-Posedness of a Coupled Camassa-Holm System in Critical Spaces

In this paper, we consider the local well-posedness of a coupled Camassa-Holm system with initial data in Besov spaces B^s_{2,1} with critical index s=\frac{3}{2}.

Global mild solutions of the micropolar fluid system in critical spaces

We prove the global in time existence of a small solution for the 3D micropolar fluid system in critical Fourier–Herz spaces by using the Fourier localization method and Littlewood–Paley theory.

Well-posedness for a modified two-component Camassa-Holm system in critical spaces

This paper is concerned with the problem of well-posedness for a modified two-component Camassa-Holm system in Besov spaces with the critical index $s=\frac 3 2$.

Global existence for the magnetohydrodynamic system in critical spaces

In this article, we show that the magnetohydrodynamic system in . We also prove that the constructed solution exists globally in time if the initial data are small. In particular, this allows us to work in the framework of Besov space with negative regularity indices and this fact is particularly important when the initial data are strongly oscillating.

Asymptotic decay for the solutions of the parabolic–parabolic Keller–Segel chemotaxis system in critical spaces

We consider the classical parabolic–parabolic Keller–Segel system describing chemotaxis, i.e., when both the evolution of the biological population and the chemoattractant concentration are described by a parabolic equation. We prove that when the equation is set in the whole space R d and dimension d ≥ 3 the critical spaces for the initial bacteria density and the chemical gradient are respectively L a ( R d ) , a > d / 2 , and L d ( R d ) . For in these spaces, we prove that small initial data give rise to global solutions that vanish as the heat equation for large times and that exhibit a regularizing effect of hypercontractivity type.

A cost effective critical space systems design approach

NASA-ISC requires avionics platforms capable of serving a wide range of applications in a cost-effective manner. In part, making the avionics platform cost effective means adhering to open standards and supporting the integration of COTS products with custom products. Inherently, operation in space requires low power, mass, and volume while retaining high performance, reconfigurability, scalability, and upgradability. The Universal Mini-Controller (UMC) project is based on a modified PC/104-Plus architecture while maintaining full compatibility with standard COTS PC/104 products. The architecture consists of a library of stackable building block modules, which can be mixed and matched to meet a specific application. A set of NASA developed core building blocks, (e.g. processor card, analog input/output card, high level analog card, and a Mil-Std-1553 card) were constructed to meet critical functions and unique interfaces.