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In this paper, we are concerned with the motion of electrically conducting fluid governed by the two-dimensional non-isentropic viscous compressible MHD system on the half plane with no-slip condition on the velocity field, perfectly conducting wall condition on the magnetic field and Dirichlet boundary condition on the temperature on the boundary. When the viscosity, heat conductivity and magnetic diffusivity coefficients tend to zero in the same rate, there is a boundary layer which is described by a Prandtl-type system. Under the non-degeneracy condition on the tangential magnetic field instead of monotonicity of velocity, by applying a coordinate transformation in terms of the stream function of magnetic field as motivated by the recent work [27] , we obtain the local-in-time well-posedness of the boundary layer system in weighted Sobolev spaces.

For the two-dimensional Magnetohydrodynamics (MHD) boundary layer system, it has been shown that the non-degenerate tangential magnetic field leads to the well-posedness in Sobolevspaces and high Reynolds number limits without any monotonicity condition on the velocity field in our previous works.This paper aims to show that sufficient degeneracy in thetangential magnetic field at a non-degenerate critical point of the tangential velocity field of shear flow indeed yields instability as for the classical Prandtl equations without magnetic field studied by Gerard-Varet and Dormy (2010). This partially shows the necessity of thenon-degeneracy in the tangential magnetic field for the stability of the boundary layer of MHD in 2D at least in Sobolev spaces.

This paper is concerned with the stability of boundary layer solutions for a viscous hyperbolic system transformed via a Cole--Hopf transformation from a singular chemotactic system modeling the in...

Motivated by the paper Gerard-Varet and Dormy (2010) [6] [JAMS, 2010] about the linear ill-posedness for the Prandtl equations around a shear flow with exponential decay in normal variable, and the recent study of well-posedness on the Prandtl equations in Sobolev spaces, this paper aims to extend the result in [6] to the case when the shear flow has general decay. The key observation is to construct an approximate solution that captures the initial layer to the linearized problem motivated by the precise formulation of solutions to the inviscid Prandtl equations.

The well-posedness of the three space dimensional Prandtl equations is studied under some constraint on its flow structure. Together with the instability result given in [28] , it gives an almost necessary and sufficient structural condition for the stability of the three-dimensional Prandtl equations. It reveals that the classical Burgers equation plays an important role in determining this type of flow with special structure, that avoids the appearance of the secondary flow, an unstabilizing factor in the three-dimensional Prandtl boundary layers. And the sufficiency of the monotonicity condition on the tangential velocity field for the existence of solutions to the Prandtl boundary layer equations is illustrated in the three-dimensional setting. Moreover, it is shown that this structured flow is linearly stable for any smooth three-dimensional perturbation.

This paper is concerned with the vanishing viscosity limit for the incompressible MHD system without magnetic diffusion effect in the half space under the influence of a transverse magnetic field on the boundary. We prove that the solution to the incompressible MHD system is uniformly bounded in both conormal Sobolev norm and \begin{document}$ L^\infty $\end{document} norm in a fixed time interval independent of the viscosity coefficient. As a direct consequence, the inviscid limit from the viscous MHD system to the ideal MHD system is established in \begin{document}$ L^\infty $\end{document}-norm. In addition, the analysis shows that the boundary layer effect is weak because of the transverse magnetic field.

In this paper, we consider the two-dimensional (2D) two-fluid boundary layer system, which is a hyperbolic-degenerate parabolic-elliptic coupling system derived from the compressible isentropic two-fluid flow equations with nonslip boundary condition for the velocity. The local existence and uniqueness is established in weighted Sobolev spaces under the monotonicity assumption on tangential velocity along normal direction based on a nonlinear energy method by employing a nonlinear cancelation technic introduced in [R. Alexandre, Y.-G. Wang, C.-J. Xu and T. Yang, J. Amer. Math. Soc., 28 (2015), 745-784; N. Masmoudi and T.K. Wong, Comm. Pure Appl. Math., 68(2015), 1683-1741] and developed in [C.-J. Liu, F. Xie and T. Yang, Comm. Pure Appl. Math., 72(2019), 63-121].

In this paper, we are concerned with the magnetic effect on the Sobolev solvability of boundary layer equations for the 2D incompressible MHD system without resistivity. The MHD boundary layer is described by the Prandtl type equations derived from the incompressible viscous MHD system without resistivity under the no-slip boundary condition on the velocity. Assuming that the initial tangential magnetic field does not degenerate, a local-in-time well-posedness in Sobolev spaces is proved without the monotonicity condition on the velocity field. Moreover, we show that if the tangential magnetic field of shear layer is degenerate at one point, then the linearized MHD boundary layer system around the shear layer profile is ill-posed in the Gevrey function space provided that the initial velocity shear flow is non-degenerately critical at the same point.

P91 steel is an important bearing material used in nuclear power plants. The study of its mechanical degradation behavior is important for ensuring safe operation. The relationship between the dislocation density of P91 steel under different strains and the corresponding nonlinear ultrasonic parameter β was studied. The dislocation density of strained samples was estimated by X-ray diffraction. Nonlinear ultrasonic testing was conducted to evaluate β, showing that this value increased with increasing dislocation density induced by different tensile elongations. It was shown that the ultrasonic second-harmonic generation technique can effectively evaluate the degradation behavior of metallic materials, and the prediction of the residual life of bearing parts in service can be made based on β and the dislocation density.

Actuality of the study and the neediest to develop rational ways for aircraft noise reducing is shown. Directions for aviation noise reduction is proposed. Analysis of the problem of aircraft noise has shown that together with increasing cargo-capacity and passenger-capacity of the civil aircraft to increase and aircraft deleterious effect on theenvironment, including the human health. The structure analysis in general and aircraft noise in particular for determining rational ways of the noise reducing is performed. The following results were obtained: the main characteristics of the aircraft noise spectrum classification, noise characteristics classification, analyzed the main sources of aircraft noise and their noise characteristics are shown. The aircraft noise specifics with depending on the flight stage is given. The main ways to reduce aircraft noise proposed: improving characteristics of engines, as well as improved aerodynamic characteristics of airframe by rational choice of geometrical parameters of particular units. Keywords:aircraft noise, noiselevel, noise intensity, noise frequency, noise reduction, protective coverage.

In this paper, we give an instability criterion for the Prandtl equations in three-dimensional space, which shows that the monotonicity condition on tangential velocity fields is not sufficient for the well-posedness of the three-dimensional Prandtl equations, in contrast to the classical well-posedness theory of the two-dimensional Prandtl equations under the Oleinik monotonicity assumption. Both linear stability and nonlinear stability are considered. This criterion shows that the monotonic shear flow is linearly stable for the three-dimensional Prandtl equations if and only if the tangential velocity field direction is invariant with respect to the normal variable, and this result is an exact complement to our recent work (A well-posedness theory for the Prandtl equations in three space variables. arXiv:1405.5308 , 2014) on the well-posedness theory for the three-dimensional Prandtl equations with a special structure.

In this paper, we study the asymptotic behavior for the incompressible anisotropic Navier–Stokes equations with the non-slip boundary condition in a half space of \({\mathbb{R}^3}\) when the vertical viscosity goes to zero. Firstly, by multi-scale analysis, we formally deduce an asymptotic expansion of the solution to the problem with respect to the vertical viscosity, which shows that the boundary layer appears in the tangential velocity field and satisfies a nonlinear parabolic–elliptic coupled system. Also from the expansion, it is observed that away from the boundary the solution of the anisotropic Navier–Stokes equations formally converges to a solution of a degenerate incompressible Navier–Stokes equation. Secondly, we study the well-posedness of the problems for the boundary layer equations and then rigorously justify the asymptotic expansion by using the energy method. We obtain the convergence results of the vanishing vertical viscosity limit, that is, the solution to the incompressible anisotropic Navier–Stokes equations tends to the solution to degenerate incompressible Navier–Stokes equations away from the boundary, while near the boundary, it tends to the boundary layer profile, in both the energy space and the L∞ space.

We study the well-posedness theory for the MHD boundary layer. The boundary layer equations are governed by the Prandtl type equations that are derived from the incompressible MHD system with non-slip boundary condition on the velocity and perfectly conducting condition on the magnetic field. Under the assumption that the initial tangential magnetic field is not zero, we establish the local-in-time existence, uniqueness of solution for the nonlinear MHD boundary layer equations. Compared with the well-posedness theory of the classical Prandtl equations for which the monotonicity condition of the tangential velocity plays a crucial role, this monotonicity condition is not needed for MHD boundary layer. This justifies the physical understanding that the magnetic field has a stabilizing effect on MHD boundary layer in rigorous mathematics., Comment: 34 pages

Needle is a kind of basic medical instruments in minimally invasive surgery. A thin and long needle is inserted into a human body through the skin to perform diagnosis and treatment tasks. In order to improve the steerability of a needle, articulated needle is proposed in this paper. An articulated needle consists of a head with a bevel-tip, several articulations and several sections. Articulations are much easier to be bent, which allows proposed articulated needle to be more easily controlled to achieve a complex curved trajectory. The structure of the articulated needle is investigated for improving its bending performance. The influences of the angle of bevel-tip, the sectional dimension of sections, the number of articulations, the maximum bending angle of articulations, and the distribution of articulations on the bending performance of the needle are studied, which provide the basis for path planning and navigation of an articulated needle.

As for the difficulties in the water injection profile controlling in the offshore oilfields, a kind of polyacrylamide emulsion and its relative profile controlling system were developed in this study. Laboratory experiments have shown that the dissolution time of the emulsion polymer into the sea water is less than 15 minutes, and the viscosity of the polymer solution is larger than 15 mPa·s when the polymer concentration is 2000 mg/L under the temperature of 70°C. The viscosity of the polymer crosslinking system is larger than 150 mPa·s, and the modulus elasticity of the crosslinking system is larger than 500 mPa. A pilot test on two wells from the Shengli Chengao Oilfield was conducted to verify the practical application performance of the emulsion polymer. The pilot test shows that after 2 months emulsion polymer injection, the bottomhole pressure of the production wells has increased by 1.48-1.79 MPa, the oil production from one correspondent well has increased from 28.67 t/d to 35.8 t/d, and the water content in the production flow has decreased from 52.3% to 41.7%. It is believed that the developed emulsion polymer and its crosslinking system have a wide application to the development of Shengli offshore fields.

The global existence of weak solutions to the three space dimensional Prandtl equations is studied under some constraint on its structure. This is a continuation of our recent study on the local existence of classical solutions with the same structure condition. It reveals the sufficiency of the monotonicity condition on one component of the tangential velocity field and the favorable condition on pressure in the same direction that leads to global existence of weak solutions. This generalizes the result obtained by Xin-Zhang on the two-dimensional Prandtl equations to the three-dimensional setting., Comment: 20 pages