This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.See Answer Question: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F around the...
Cis the circlex2+y2=1,z=4. There are 2 steps to solve this one.
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...
Finally, in Section 4 we prove the main a priori estimates needed to study the convergence and finally in Section 5 we prove Theorem 1.1. 2. Notations and preliminaries In this section we declare the notation we will use in the paper, we recall the main definitions concerning weak solutions...
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Thus we will conclude that Theorem 2.8 is applicable. Our aim in this subsection is to study the following stochastic Navier–Stokes equations in O(2.12){du+{νAu+B(u)}dt=fdt+dW(t),t⩾0,u(0)=x, where we assume that x∈H, f∈V′ and W(t), t∈R, is a two-sided ...
We consider various numerical examples to test Algorithm A and to confirm the error estimates derived in Theorem 3.4. In Examples 1–3 we consider the Stokes problem formulated in Section 2.2 where wR,h=0 and dh=0, in Example 4 we test numerical simulations for various viscous numbers, and...
The Gauss–Lobatto variant of the DGSEM is of interest because it satisfies the SBP–SAT property, enabling Gauss's divergence theorem to be reproduced discretely, which makes it possible to follow all the steps in the continuous entropy analysis, now in a discrete context, through the use of...
There are many choices of the smoothing factor 𝑠𝜖 that satisfy the three conditions given by (20) of Theorem 1. Recalling that 𝑠𝜖(𝑟)=𝑠1(𝑟/𝜖), Table 1 summarizes four smoothing factors 𝑠1 hereafter employed as examples. These smoothing factors were chosen due to their...
Theorem 4.4 Under the assumptions of Theorem 4.3, we have(4.13)‖u−uh‖0≤Ch2(‖u‖2+‖p‖1). Proof Multiplying the first and second equations of system (4.11) by e=u−uh and η=p−ph, respectively, integrating the resulting equations over the domain Ω, using Green’s formula...