English

In this paper, through maximal regularity estimates for the Stokes equation, we study the local well-posedness of strong solutions to the 3D MHD equations with Hall and ion-slip effects under the condition that the initial data $$(u_0,B_0 )\in H^{\frac{1}{2}+\varepsilon }({\mathbb {R}}^3)\times H^2({\mathbb {R}}^3) $$ and any $$\varepsilon \in (0,1)$$. This is an improvement of the recent results given by Fan et al. (Z Angew Math Phys, 2015).

In this paper we prove the local well-posedness of strong solutions to a chemotaxis-shallow water system with initial vacuum in a bounded domain Ω ų ℝ2 without the standard compatibility condition for the initial data. This improves some results obtained in [J. Differential Equations 261(2016), 6758–6789].

In this paper, we first prove the local well-posedness of strong solutions to the incompressible Hall-MHD system for initial data $$(u_0,B_0)\in H^{\frac{1}{2}+\sigma }({\mathbb {R}}^3)\times H^{\frac{3}{2}}({\mathbb {R}}^3)$$ with $$\sigma \in (0,2)$$ . In particular, if the viscosity coefficient is equal to the resistivity coefficient, we can reduce $$\sigma $$ to 0 with the aid of the new formulation of the Hall-MHD system observed by Danchin and Tan (Commun Partial Differ Equ 46(1):31–65, 2021). Compared with the previous works, our local well-posedness results improve the regularity condition on the initial data. Moreover, we establish the global well-posedness for small initial data in $$H^{\frac{1}{2}+\sigma }({\mathbb {R}}^3)\times H^{\frac{3}{2}}({\mathbb {R}}^3)$$ with $$\sigma \in (0,2)$$ , and get the optimal time-decay rates of solutions.

In this work, we prove the local well-posedness of strong solutions to the isentropic compressible magnetohydrodynamics system with vacuum in a bounded domain Ω⊂R3.

Existence theorem and blow-up criterion of the strong solutions to the two-fluid MHD equation in [formula omitted

In this paper, we consider the Cauchy problem for a highly nonlinear shallow water model arising from the full water waves with Coriolis effect. The existence of weak solutions to the equation in the lower order Sobolev space Hs(R) with 1<s≤32 is presented. Moreover, the local well-posedness of strong solutions in Sobolev space Hs(R) with s>32 is established by the pseudoparabolic regularization technique.

Local well-posedness of strong solutions to the 2D nonhomogeneous primitive equations with density-dependent viscosity

Preparation and regulation of AlCrNiTiSi high entropy alloy coating by a multi-arc magnetic filter cathode vacuum arc system

This work presents a study of the hydrodynamics of gas bubbles in a magnetic fluid which is in a flat channel with a thickness of 2 mm, placed in the non-uniform field of the rare-earth annular permanent magnet. The peculiarity of the magnetic field configuration of this magnet is as follows: at a distance of 9 mm from the surface of the magnet there are two symmetric regions where the magnetic field is zero, the so-called ‘magnetic vacuum’ regions. The specified configuration of the magnetic field allows capturing and holding gas cavities when the magnet moves; while pressing the cavity to the bottom of the channel, gas bubbles separate. An experimental setup was created to study the hydrodynamics of gas inclusions; using this setup studies on the concentration series of four magnetic fluids based on kerosene with a volume concentration of 10.56 %; 6.32 %; 3.93 % and 2.08% were conducted. The mechanism of gas bubbles capturing and gas cavity formation in a magnetic fluid in the magnetic vacuum region of an annular magnet is investigated. The process of the separation of the bubbles from the air cavity when it is pressed down to the bottom of the channel by a non-uniform magnetic field is studied.

We assess the toroidal magnetic field B t asymmetry in DIII-D due to a misalignment of the toroidal field coils with respect to the poloidal magnetic field coils and vacuum vessel. The peak-to-peak variation of the divertor strike point (SP) radius is measured to be 1 cm, with an n = 1 toroidal pattern. We use the centre of a narrow carbon deposition band on tungsten-coated divertor tiles just inside the outer strike point (OSP) as a proxy for the divertor SP location. The band occurred in a series of reverse B t discharges with the OSP positioned on the divertor inserts due to strong E × B drift transport of C from the inner to the outer SP through the private flux region. The variation in band radius (and hence the magnetic SP) is a (4.89 ± 0.31) mm shift toward (310 ± 4)° toroidal direction. These measurements agree well with previous measurements of the 3D magnetic field distribution (Luxon 2003 Nucl. Fusion 43 1813), simulations performed by the mafot field line integration code, and recent Langmuir probe measurements in the small-angle-slot (SAS) divertor (Watkins et al 2019 Nucl. Mater. Energy 18 46). Comparison of these measurements in the SAS divertor also indicates that there is the possibility of a tilt (in conjunction with the shift) of the B t coil field of (0.04 ± 0.07)° towards the toroidal angle of (215 ± 25)°. Previous measurements suggested a field misalignment of (4.6 ± 0.3) mm in the 270° toroidal direction, and a tilt of (0.06 ± 0.02)° toward the 114° toroidal direction, which is similar to the results reported here. These studies will be important for better understanding the radial variation of the toroidal strike line in DIII-D, for designing the new generation of SAS divertor, and for developing an understanding of the impact of error fields on tokamaks with tightly baffled slot divertors.

We consider a free boundary problem for the axially symmetric incompressible ideal magnetohydrodynamic equations that describe the motion of the plasma in vacuum. Both the plasma magnetic field and vacuum magnetic field are tangent along the plasma-vacuum interface. Moreover, the vacuum magnetic field is composed in a non-simply connected domain and hence is non-trivial. Under the non-collinearity condition for the plasma and vacuum magnetic fields, we prove the local well-posedness of the problem in Sobolev spaces.

Problem. Substations 10(6)/0.4 kV built into residential buildings create a magnetic field with magnetic flux density of more than 10 μT in nearby residential premises, which is a danger to the health of the population and makes the study of this magnetic field relevant for the development of methods for its protection. The main source of the substations external magnetic field is their low-voltage current conductor, the contribution of which to the total level of the magnetic field is more than 90 %. Multi-dipole mathematical models, which have a clear physical interpretation, are a promising method of modeling the substations magnetic field, which is important for the further development of methods of population protection. The purpose of the work is to modify the well-known multi-dipole model for calculation based on it with a limited error of the external magnetic field of current conductors of built-in substations that are close to residential buildings at a distance of up to one meter. Methodology. A modified two-phase multi-dipole mathematical model of the main source of the external magnetic field of substation – its three-phase low-voltage current conductors – is proposed, which, unlike the existing model, is based on a two- you to halve the distance to the area of calculation without increasing the error. Verification. An experimental verification of the modified two-phase multi-dipole model of the magnetic field of a three-phase 100 kVA transformer substation on its full-scale physical model was carried out, and the results of the experiment were presented, confirming the coincidence of the calculation and the experiment with a spread of no more than 7 %.

The energetics of the long duration GRB phenomenon is compared with models of a rotating BH in a strong magnetic field generated by an accreting torus. The GRB energy emission is attributed to magnetic field vacuum breakdown that gives origin to a e ± fireball. Its subsequent evolution is hypothesized in analogy with the in‐flight decay of an elementary particle. An anisotropy in the fireball propagation is thus naturally produced. The recent discovery in some GRB of an initial phase characterized by a thermal spectrum could be interpreted as the photon emission of the fireball photosphere when it becomes transparent. In particular, the temporal evolution of the emission can be explained as the effect of a radiative deceleration of the out‐moving ejecta.

The magnetic fields of neutron stars and some related effects

The electromagnetic response of the Moon to excitation by the time dependent fluctuations of the interplanetary magnetic field is given for the dark or antisolar hemisphere of the Moon. Six hours of time series data from the Explorer 35 magnetometer and the lunar surface magnetometer on Apollo 12 are used to obtain the Fourier spectral amplitudes of the surface and interplanetary fields from which transfer functions are calculated for the east-west, north-south, and vertical directions at the Apollo site. A critical discussion of lunar conductivity profiles derived from night side radial magnetic field data and vacuum scattering theory is presented. Limitations are shown that there is no evidence for a lunar core as conducting as 0.01 mhos/m.