On the conservation laws and the structure of the nonlinearity for SQG and its generalizations
Using a new definition for the nonlinear term, we prove that all weak solutions to the SQG equation (and mSQG) conserve the angular momentum. This result is new for the weak solutions of [Resnick, '95] and rules out the possibility of anomalous dissipation of angular momentum. We also prove con...
Saved in:
Published in | arXiv.org |
---|---|
Main Authors | , |
Format | Paper |
Language | English |
Published |
Ithaca
Cornell University Library, arXiv.org
13.03.2024
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | Using a new definition for the nonlinear term, we prove that all weak solutions to the SQG equation (and mSQG) conserve the angular momentum. This result is new for the weak solutions of [Resnick, '95] and rules out the possibility of anomalous dissipation of angular momentum. We also prove conservation of the Hamiltonian under conjecturally optimal assumptions, sharpening a well-known criterion of [Cheskidov-Constantin-Friedlander-Shvydkoy, '08]. Moreover, we show that our new estimate for the nonlinearity is optimal and that it characterizes the mSQG nonlinearity uniquely among active scalar nonlinearities with a scaling symmetry. |
---|---|
ISSN: | 2331-8422 |