# Tagged Questions

In vector calculus, a vector field is an assignment of a vector to each point in a subset of space. A vector field in the plane, for instance, can be visualized as a collection of arrows with a given magnitude and direction each attached to a point in the plane. Vector fields are often used to model,...

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### $f:M\to N$ smooth manifold map. $F(x)=(x,f(x))\in M\times N$. For each $X\in \mathfrak{X}(M)$ there's a F-related $Y\in \mathfrak{X}(M\times N)$.

Let $M$ and $N$ be to manifolds and $f:M\to N$ smooth map. Define $F:M\to M\times N$ by $F(x)=(x,f(x))$. Show that for each $X\in \mathfrak{X}(M)$ there's a F-related $Y\in \mathfrak{X}(M\times N)$. ...
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### Existence of closed level sets on a surface for some field

Consider an infinite 3D space with only 2 things in it: wind and a solid object. Wind evidently blows around this solid object over its rigid surface. Bascially we are trying to set up a pure field. ...
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### What is the difference between $(A\cdot\nabla )B$ and $A(\nabla\cdot B)$?

What is the difference between $(A\cdot\nabla )B$ and $A(\nabla\cdot B)$, where $A$ and $B$ are two vectors. My guess is that $(A\cdot\nabla )B$ means the vector $A$ is being multiplied by the rate ...
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### Equality of vector & Directions

Is the direction 120° west of the South Axis same as the direction 30° north of the West Axis (both from a fixed observational point).
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### Stationary solutions in dissipative fields

I am trying to solve the following exercise: Let $F:\mathbb R^d \rightarrow \mathbb R^d$ a continuous and locally Lipschitz vector field. We say that $F$ is dissipative if and only if there exists ...