Finding Conservation Laws

In joint work with Sal, we have finally written down the systematic process for deriving all of Olver’s conservation laws for the water-wave problem from our nonlocal-nonlocal formulation. This post outlines the current state of deriving the conservation laws from this Nonlocal-Nonlocal formulation discussed in the A Weak Formulation of Water Waves in Surface Variables. Click Continue Reading… to learn a little bit more about the process.

Snapshot of fluid domain
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Thinking more about multiple scales

[mathjax] Perhaps this is widely known, but I got a bit stuck-in-the-weeds thinking about applying multiple scales to problems with nonlocal operators. I have honestly been a bit unsatisfied with the literature that I have found on this scenario – that said, if you have any suggestions or references, please feel free to leave them in the comments! Continue reading to see what I’ve been thinking about.

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