Is This Variant of the Navier-Stokes Equation Solvable?

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SUMMARY

The discussion centers on the solvability of a variant of the Navier-Stokes equations, which are partial differential equations crucial in fluid dynamics. Participants highlight the complexity of the equation, particularly the interpretation of the function "P" and the variable "g." It is established that libraries exist for solving these equations, suggesting that individuals should focus on understanding the equations and the methodologies for solving them rather than attempting to solve them independently.

PREREQUISITES
  • Understanding of partial differential equations
  • Familiarity with the Navier-Stokes equations
  • Knowledge of differential operators, specifically the gradient operator
  • Experience with computational fluid dynamics libraries
NEXT STEPS
  • Research existing libraries for solving Navier-Stokes equations, such as OpenFOAM
  • Study the mathematical properties of partial differential equations
  • Explore numerical methods for fluid dynamics simulations
  • Learn about the implications of the variable "g" in fluid dynamics contexts
USEFUL FOR

This discussion is beneficial for mathematicians, physicists, and engineers specializing in fluid dynamics, as well as students and researchers looking to deepen their understanding of the Navier-Stokes equations and their applications.

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.
 

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