Uniqueness of higher integrable solution to the Landau equation with Coulomb interactions

Jann-Long Chern; Maria Gualdani

Uniqueness of higher integrable solution to the Landau equation with Coulomb interactions

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arxiv 1910.06216 v2 pith:HOIBU72U submitted 2019-10-14 math.AP

Jann-Long Chern , Maria Gualdani This is my paper · ORCID

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keywords solutioncoulombequationinteractionslandauuniquenessassumptionbounded

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abstract

We are concerned with the uniqueness of weak solution to the spatially homogeneous Landau equation with Coulomb interactions under the assumption that the solution is bounded in the space $L^\infty(0,T,L^p(\R^3))$ for some $p>3/2$. The proof uses a weighted Poincar\'e-Sobolev inequality recently introduced in \cite{GG18}.

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Weak-strong uniqueness for the Landau equation by a relative entropy method
math.AP 2025-05 accept novelty 7.0 of 10

For the Landau equation with soft potentials (including Coulomb), this paper proves that all H-solutions with enough moments coincide with the smooth solution, via a relative entropy estimate.

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