# Questions tagged [fluid-dynamics]

For questions about fluid dynamics which studies the flows of fluids and involves analysis and solution of partial differential equations like Euler equations, Navier-Stokes equations, etc. Tag with [tag:mathematical-physics] if necessary.

1,117 questions
Filter by
Sorted by
Tagged with
32 views

### Existence of Smooth Periodic Solutions for Navier-Stokes Equations in Three Dimensions [closed]

This paper establishes the existence of smooth periodic solutions for the Navier-Stokes equations in three-dimensional space. The Navier-Stokes equations describe the motion of incompressible viscous ...
22 views

### How do I find the absolute maximum and minimum values of the Lamb-Oseen Vortex?

I am researching alternative solutions to Stokes equations and I came across a problem with the Lamb-Oseen vortex I cannot solve that I hope will allow easier derivations of vortex functions with ...
23 views

### Exercise 7.6 of Robinson, Rodrigo, Sadowski: Smoothness of Navier-Stokes on Bounded Domains

My question is about Exercise 7.6 of the excellent book 'The Three-Dimensional Navier-Stokes Equations' by Robinson, Rodrigo and Sadowski. More generally, it is about higher regularity in space of ...
20 views

### Space of functions, Banach spaces, reference books to find basic properties of Bochner integral, Laplace and Fourier transforms.

I'm looking for references where I can find definitions and basic properties of Bochner Integral in Banach Spaces and its basic properties, such as: Every continuous function is integrable, ...
• 369
84 views

• 1,393
39 views

### Interpretation of the timescale non-dimensionalizing $\partial_t c(x,t) = - \frac{\dot{s}x}{s}\partial_x c + D \partial_x^2c$

Background: A thin filament of fluid mixes into a flow field in accord with the so-called "compression-diffusion equation" (CDE), which is essentially an advection-diffusion equation with a ...
• 1,454
26 views

### Divergence of a Point

I am currently reading a book titled Notes on Computational Fluid Dynamics: General Principles, which is provided by OpenFOAM at https://doc.cfd.direct/notes/cfd-general-principles/contents. In ...
5 views

### Calculation of density distribution function for infinite (in x and y) static isothermal slab supported by gas pressure and it's own gravity

Let us cosider an infinite (in x and y) static isothermal slab, symmetric about z = 0, supported by gas pressure and under it's own gravity. No other forces are acting. To calculate the density ...
• 37
57 views

### Navier Stokes Eqns: Boundary Conditions and Pressure Coupling

I have made it a personal long-term goal of mine to numerically solve the 1D transient Navier-Stokes equations for simple incompressible and compressible flow scenarios. I want to do it for a few ...
22 views

• 131
63 views

• 155
30 views

### Indeterminate Form for Partial Derivative of Flow Variables

The following is a paraphrased version of the derivation within John D. Anderson's Fundamentals of Aerodynamics's section on the Method of Characteristics: The exact governing equation for two-...
• 177
42 views

### Integrating by Parts $\int\limits^{2}_{0}pydy$ - A calculation related to flowrate.

Happy new year everyone! I have a question that I struggle related to integration by parts. Suppose I'm going to solve the following using integration by parts. $$\int\limits^{2}_{0}pydy$$ Where $p$ ...
• 1,626
76 views

### vector field PDE sandwich theorem

Consider the vector valued system of PDE's for $\textbf{f} = [f_1,f_2,f_3]$ and $\textbf{g} = [g_1,g_2,g_3]$ \dfrac{\partial}{\partial t}\textbf{f}- F\left(\textbf{f}, \nabla f_i, \...
• 235
117 views

• 177
26 views

• 63
1 vote
43 views

### Solving for constants of integration continuously resulting in trivial statement 0=0

I am attempting to solve a fairly simply pair of ODEs that represent a flow field for a fluid dynamics problem. I am attempting to find the particle path but I am getting stuck trying to find x and y ...
1 vote
I'm trying to prove the symmetry of the isotropic tensor in the linear relation between the shear stress and strain rate for Newtonian fluid T_{ij}=\beta_{ijlm}\frac{\partial u_{l}}{\partial x_{m}}.\$...