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Defocusing semilinear wave equation

Morawetz identity for the defocusing wave equation

{c}

For a finite-energy defocusing power-wave solution in three dimensions,
$$
\int_0^\infty\int_{\mathbb R^3}\frac{|u(t,x)|^{p+1}}{|x|}\,dx\,dt
\lesssim E(u(0)).
$$
Hardy's inequality bounds the Morawetz action by the conserved energy.


Morawetz estimate for the defocusing wave equation

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 154 / 2 / 4 / Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 154 / 2 / 7 / Solution

Morawetz estimate for the defocusing wave equation

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Morawetz estimate for the defocusing wave equation

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