1.2 MHD方程组的研究背景 磁流体动力学(Magnetohydrodynamics,简称MHD)是研究等离子体和磁场相 互作用的物理学分支,其基本思想是在运动的导电流体中,磁场能够感应出电流.磁流体动力学将等离子体作为连续介质处理,要求其特征尺度远远大于粒子的平均 自...
2 Summing for all K Theorem 5. There exists a constant β independent of h such that: (divv, p) = sup v 1,? v ∈U 0 h divv pdx ? sup 0 v ∈Uh v 1, ? ≥β p 0,? , p ∈ P2h , (13) and the solution of (4) exists uniquely. Proof. Since p ∈ L2 0 (?) there...
The linear Stokes operator associated to the various boundary conditions is first studied. Then a classical fixed-point theorem is used to show how the properties of the operator lead to local solutions or global solutions for small initial data....
We now use Green’s theorem in the plane to evaluate the line integral. Applying Eq. (6.46) with P=-x and Q=y, the integral reduces to -2∫dA=-2π. Returning next to the surface integrals of ∇×B, the integral for the disk, Case (1), is ∫disk(∇×B)·eˆzdA=-2∫...
The stabilisation parameters \alpha _1 and \alpha _2 have been chosen, for simplicity, to be equal while \alpha _2 is close to its upper bound, as given by Theorem 2. Fig. 8 The magnitude of the tangential Lagrange multiplier on the top and the bottom boundaries for the curved ...
By symbolic logical method, prove the existing of Stokes’ Theorem in countless discretional parametrized surface coordinates (include orthogonal curve coordinates and nonorthogonal curve coordinates), spread closed curve integral and surface integral to countless discretional parametrized surface coordinates, rea...
3 Boundary value problems for abstract elliptic equations In this section, we derive the maximal regularity properties of problem (1.7). BVPs for DOEs were studied, e.g., in [9, 11, 13–19]. For references, see, e.g., [19]. From [[18], Theorem 4.1] we have the following result...
A Liouville theorem for the axially-symmetric Navier-Stokes equations. J Funct Anal, 2011, 261: 2323–2345 60 Lei Z, Zhang Q. Criticality of the axially symmetric Navier-Stokes equations. Pacific J Math, 2017, 289: 169–187 61 Wei D. Regularity criterion to the axially symmetric Navier-...
we study existence and uniqueness of solutions to the stationary Stokes and Navier–Stokes problems under convexity assumption for the connected components of boundary given the conditions for rotation, pressure and normal derivative of velocity (Theorem 4.1, Theorem 4.2, Theorem 4.3, Theorem 4.4). Re...
In our setting (1.1), we do not take into account of the gravity force nor the surface tension.Footnote1 Free boundary problems for incompressible fluids were first considered by Solonnikov [54] in the space-timesetting and he proved the time local well-posedness of the initial boundary valu...