Learn the definition of Stokes theorem and browse a collection of 81 enlightening community discussions around the topic.
However there are several examples I can find, where this doesn't make sense. My... NicolaiTheDane Thread Mar 23, 2018 Stokes Replies: 7 Forum: Calculus C Faraday's Law and Stokes Theorem Homework Statement Homework Equations Stokes Theorem The Attempt at a Solution I'm having a ...
It is shown that the application of the non-Abelian Stokes theorem to the computation of the operators constructed with Wilson loop will lead to ambiguity if the gauge field under consideration is nontrivial. This point is illustrated by the specific examples of the computation of a nonlocal ...
Theorem 1 If is a classical solution to Navier-Stokes on with for some , then and for and . As a corollary, one can now improve the Escauriaza-Seregin-Sverak blowup criterion to for some absolute constant , which to my knowledge is the first (very slightly) supercritical blowup criteri...
Answer to: Verify Stokes's theorem for the vector field A = Rcos theta + Phi sin theta by evaluating it on the hemisphere of unit radius. By...
The dynamics near an equilibrium was discussed in Section 2 (Theorem 2.2), it can be studied for a general 3D problem. In the remaining examples, the system possesses a symmetry that allows to reduce the dimensionality. The dynamics of the symmetric solutions can be described by equations with...
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 ...
To prove Theorem 1 we will first consider the family of equations with homogeneous boundary conditions $$\begin{aligned} \begin{array}{ll} -\nu \Delta \mathbf {u} + \tau \nabla \Pi = \mathbf {f} &{}\quad \text {in}\ \Omega , \\ \tau \mathrm{div}\,\mathbf {u} + (1 - ...
6 Stokes’theoremTherearethreemainintegraltheoremsofvectoranalysis:Green’stheorem:∫𝜕D(Pdx+Qdy)=∫∫D(𝜕Q𝜕x−𝜕P𝜕y)dxdy;Stokes’theorem:∫𝜕SF⋅ds=∫∫S(∇×F)⋅dS=∫∫ScurlF⋅dS;Gauss’(Ostrogradsky’s,divergence)theorem:∫∫𝜕WF⋅dS=∫∫∫W(∇⋅F)dV.In...
First we prove a general spectral theorem for the linear Navier-Stokes (NS) operator in both 2D and 3D. The spectral theorem says that the spectrum consists of only eigenvalues which lie in a parabolic region, and the eigenfunctions (and higher order eigenfunctions) form a complete basis in ...