Note on the lifespan estimate of solutions for non-gauge invariant semilinear massless semirelativistic equations with some scaling critical nonlinearity
Abstract
In this manuscript, in the $L^1$ scaling critical case, a lifespan estimate of solutions to the Cauchy problem for non-gauge invariant semilinear semirelativistic equations is considered. The lifespan estimate is given by the modified test function method with a fractional Laplace operator. The main obstacle to obtaining the lifespan estimate is the non-locality of the fractional Laplace operator. To treat the non-locality, special test functions are introduced.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2021
- DOI:
- 10.48550/arXiv.2109.00030
- arXiv:
- arXiv:2109.00030
- Bibcode:
- 2021arXiv210900030F
- Keywords:
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- Mathematics - Analysis of PDEs
- E-Print:
- 9 pages