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arXiv · 2503.02570

Dynamics of dissipative solutions to the Hardy-Sobolev parabolic equation

Masahiro Ikeda·César J. Niche·Gabriela Planas
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Abstract

We study the long-time behaviour of solutions to the Hardy-Sobolev parabolic equation in critical function spaces for any spatial dimension $d \geq 5$. By employing the Fourier splitting method, we establish precise decay rates for dissipative solutions, meaning those whose critical norm vanishes as time approaches infinity. Our findings offer a deeper understanding of the asymptotic properties and dissipation mechanisms governing this equation.

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Masahiro Ikeda, César J. Niche, Gabriela Planas. 2025-03-04. Dynamics of dissipative solutions to the Hardy-Sobolev parabolic equation. https://doi.org/10.4310/dpde.260103060355

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