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## A new monotonicity formula for the spatially homogeneous Landau equation with Coulomb potential and its applications

#### Abstract

We describe a time-dependent functional involving the relative entropy and the $\dot{H}^1$ seminorm, which decreases along solutions to the spatially homogeneous Landau equation with Coulomb potential. The study of this monotone functionial sheds light on the competition between the dissipation and the nonlinearity for this equation. It enables to obtain new results concerning regularity/blowup issues for the Landau equation with Coulomb potential.

#### Domains

Mathematics [math]

### Dates and versions

hal-03867446 , version 1 (23-11-2022)

### Identifiers

• HAL Id : hal-03867446 , version 1
• ARXIV :

### Cite

Laurent Desvillettes, Ling-Bing He, Jin-Cheng Jiang. A new monotonicity formula for the spatially homogeneous Landau equation with Coulomb potential and its applications. 2022. ⟨hal-03867446⟩

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