Uniqueness of Bounded Solutions for the Homogeneous Relativistic Landau Equation with Coulomb Interactions

Abstract

We prove the uniqueness of weak solutions to the spatially homogeneous special relativistic Landau equation under the conditional assumption that the solution satisfies $(p^0{)}^{7}F(t,p)\in L^1([0,T];L^{\infty })$. The existence of standard weak solutions to the relativistic Landau equation has been shown recently in (arXiv:1806.08720)

arXiv comment37 pages, published version

References in corpus (4)

• Entropy dissipation estimates for the Landau equation in the Coulomb case and applications
• The Vlasov-Poisson-Landau System in ${\mathbb{R}}_x^3$
• On the uniqueness for the spatially homogeneous Boltzmann equation with a strong angular singularity
• Entropy dissipation estimates for the relativistic Landau equation, and applications

Cited by in corpus (5)

• The Landau equation as a Gradient Flow
• Propagation of uniform upper bounds for the spatially homogeneous relativistic Boltzmann equation
• On the Determinant Problem for the Relativistic Boltzmann Equation
• A particle method for the homogeneous Landau equation
• Propagation of $L^p$ estimates for the Spatially Homogeneous Relativistic Boltzmann Equation