Is This Variant of the Navier-Stokes Equation Solvable?

In summary, the conversation involves discussing a partial differential equation with a "partial" notation on the right and a "P()" notation on the left. The speaker is unsure if P is a function or a multiplier and also mentions a "g" that is present on the right but not the left. It is suggested that the equation is a variant of the Navier-Stokes equations and that it is not necessary to solve it oneself, but rather to learn about it and its solutions.
  • #1
mrlukey
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What the hell is this and is it solvable?
 

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  • #2
Well, it IS a "partial differential equation". Have you learned how to solve such things? The "\(\displaystyle \nabla\)" on the right is the differential operator \(\displaystyle \frac{\partial}{\partial x}+ \frac{\partial}{\partial y}+ \frac{\partial}{\partial z}\). 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?
 
  • #3
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.
 

FAQ: Is This Variant of the Navier-Stokes Equation Solvable?

What is a partial differential equation (PDE)?

A partial differential equation is a mathematical equation that involves multiple independent variables and their partial derivatives. It is used to describe physical phenomena that vary in space and time, such as heat flow, fluid dynamics, and quantum mechanics.

How do you solve a PDE?

There is no one-size-fits-all method for solving PDEs. The approach depends on the specific form of the equation and the boundary conditions. Some common techniques include separation of variables, Fourier transforms, and numerical methods.

What is the difference between a partial differential equation and an ordinary differential equation?

A partial differential equation involves multiple independent variables, while an ordinary differential equation only involves one independent variable. PDEs are used to describe systems that vary in space and time, while ODEs are used to describe systems that vary only in time.

Can all PDEs be solved analytically?

No, not all PDEs have analytical solutions. In fact, most PDEs do not have closed-form solutions and require numerical methods for approximation. However, there are some special cases where analytical solutions can be found, such as for linear PDEs with simple boundary conditions.

What are some real-world applications of PDEs?

PDEs have a wide range of applications in various fields such as physics, engineering, and economics. Some examples include modeling heat transfer in a building, predicting weather patterns, and simulating fluid flow in an airplane engine. PDEs are also used in financial mathematics to model stock prices and interest rates.

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