MHB Is This Variant of the Navier-Stokes Equation Solvable?

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The discussion centers on a variant of the Navier-Stokes equations, which are a type of partial differential equation. There is confusion regarding the notation used, specifically the meaning of "P( )" and the absence of "g" on the left side of the equation. Participants suggest that solving such equations typically requires specialized libraries rather than individual effort. Understanding the equations and their solutions is emphasized as more important than attempting to solve them independently. Overall, the solvability of this variant remains uncertain without further clarification on its components.
mrlukey
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What the hell is this and is it solvable?
 

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Well, it IS a "partial differential equation". Have you learned how to solve such things? The "[math]\nabla[/math]" on the right is the differential operator [math]\frac{\partial}{\partial x}+ \frac{\partial}{\partial y}+ \frac{\partial}{\partial z}[/math]. I have a little problem with the left side. It is not clear to me whether that "P( )" means that P is a function of the quantity in the parentheses or whether it just means P times that quantity. Also there is a "g" on the right but not on the left. Is there another part of the problem that defines g?
 
mrlukey said:
What the hell is this and is it solvable?
It looks like a variant of the Navier-Stokes equations.
They've written libraries about how to solve them.
I do not think you are supposed to solve them yourself. Likely you're supposed to learn about what it is and what some ways to solve them are.
 
Thread 'Problem with calculating projections of curl using rotation of contour'

Thread 'Problem with calculating projections of curl using rotation of contour'

Hello! I tried to calculate projections of curl using rotation of coordinate system but I encountered with following problem. Given: ##rot_xA=\frac{\partial A_z}{\partial y}-\frac{\partial A_y}{\partial z}=0## ##rot_yA=\frac{\partial A_x}{\partial z}-\frac{\partial A_z}{\partial x}=1## ##rot_zA=\frac{\partial A_y}{\partial x}-\frac{\partial A_x}{\partial y}=0## I rotated ##yz##-plane of this coordinate system by an angle ##45## degrees about ##x##-axis and used rotation matrix to...
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