Fdtxjr

Multi tool use

Why is there an extra space when I type "ls" on the Desktop?

School performs periodic password audits. Is my password compromised?

Why do we call complex numbers “numbers” but we don’t consider 2-vectors numbers?

Is "cogitate" used appropriately in "I cogitate that success relies on hard work"?

What is Tony Stark injecting into himself in Iron Man 3?

A vote on the Brexit backstop

What is the orbit and expected lifetime of Crew Dragon trunk?

Inorganic chemistry handbook with reaction lists

Too soon for a plot twist?

What does it take to become a wilderness skills guide as a business?

Is this a crown race?

Is there a logarithm base for which the logarithm becomes an identity function?

Vector-transposing function

Was this cameo in Captain Marvel computer generated?

I am the light that shines in the dark

How does learning spells work when leveling a multiclass character?

How would an energy-based "projectile" blow up a spaceship?

I've given my players a lot of magic items. Is it reasonable for me to give them harder encounters?

Paper published similar to PhD thesis

Should we avoid writing fiction about historical events without extensive research?

Unidentified signals on FT8 frequencies

Did Amazon pay $0 in taxes last year?

Boss Telling direct supervisor I snitched

Should I file my taxes? No income, unemployed, but paid 2k in student loan interest

Phase difference between variables in a PDE

Problem with Laplacian while treating polar coordinates as special case of spherical coordinates.Chain Rule in Polar coordinatesDot product of gradient and tangent vectorDifference of Entropy of two-dimensional Gaussians2nd Order PDE with Mixed DerivativesProof of vector identity from vorticity transport equationPDE Cartesian/Polar forms and Numerical Solver issuesLaplacian operator and divergence at the origin$nablaint_S_1(0) f(|x|w)dsigma(w) = int_S_1(0) nabla f(|x|w)dsigma(w)$Grad in polar coordinates

1

$begingroup$

For a given vector $boldsymbolu = (u,v,w)$, in a polar coordinate system $(x,r,theta)$, I have read that the divergence free equation:
begingather
nabla cdot boldsymbol u equiv
fracpartial upartial x + frac1rfracpartialpartial r(vr) + frac1rfracpartial wpartial theta = 0
endgather
shows that the phase difference between the components $u$ and $v$ is $pi/2$. How can I prove this?

I have tried representing each of the variables in polar form, and tried obtaining the phase difference between them but with no success.

complex-analysis pde polar-coordinates divergence

share|cite|improve this question

asked 15 hours ago

XoegXoeg

62

New contributor

Xoeg is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

1

$begingroup$

For a given vector $boldsymbolu = (u,v,w)$, in a polar coordinate system $(x,r,theta)$, I have read that the divergence free equation:
begingather
nabla cdot boldsymbol u equiv
fracpartial upartial x + frac1rfracpartialpartial r(vr) + frac1rfracpartial wpartial theta = 0
endgather
shows that the phase difference between the components $u$ and $v$ is $pi/2$. How can I prove this?

I have tried representing each of the variables in polar form, and tried obtaining the phase difference between them but with no success.

complex-analysis pde polar-coordinates divergence

share|cite|improve this question

asked 15 hours ago

XoegXoeg

62

New contributor

Xoeg is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

$begingroup$

For a given vector $boldsymbolu = (u,v,w)$, in a polar coordinate system $(x,r,theta)$, I have read that the divergence free equation:
begingather
nabla cdot boldsymbol u equiv
fracpartial upartial x + frac1rfracpartialpartial r(vr) + frac1rfracpartial wpartial theta = 0
endgather
shows that the phase difference between the components $u$ and $v$ is $pi/2$. How can I prove this?

I have tried representing each of the variables in polar form, and tried obtaining the phase difference between them but with no success.

complex-analysis pde polar-coordinates divergence

share|cite|improve this question

asked 15 hours ago

XoegXoeg

62

New contributor

Xoeg is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|cite|improve this question

asked 15 hours ago

XoegXoeg

62

New contributor

Xoeg is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|cite|improve this question

asked 15 hours ago

XoegXoeg

62

New contributor

Xoeg is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 15 hours ago

XoegXoeg

62

New contributor

Xoeg is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 15 hours ago

XoegXoeg

62