Existence of smooth solutions to the Landau-Fermi-Dirac equation with Coulomb potential
In this paper, we prove global-in-time existence and uniqueness of smooth solutions to the homogeneous Landau-Fermi-Dirac equation with Coulomb potential. The initial conditions are nonnegative, bounded and integrable. We also show that any weak solution converges towards the steady state given by t...
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| creator | Golding, William Gualdani, Maria Pia Zamponi, Nicola |
| description | In this paper, we prove global-in-time existence and uniqueness of smooth
solutions to the homogeneous Landau-Fermi-Dirac equation with Coulomb
potential. The initial conditions are nonnegative, bounded and integrable. We
also show that any weak solution converges towards the steady state given by
the Fermi-Dirac statistics. Furthermore, the convergence is algebraic, provided
that the initial datum is close to the steady state in a suitable weighted
Lebesgue norm. |
| doi_str_mv | 10.48550/arxiv.2107.10463 |
| format | Article |
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solutions to the homogeneous Landau-Fermi-Dirac equation with Coulomb
potential. The initial conditions are nonnegative, bounded and integrable. We
also show that any weak solution converges towards the steady state given by
the Fermi-Dirac statistics. Furthermore, the convergence is algebraic, provided
that the initial datum is close to the steady state in a suitable weighted
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solutions to the homogeneous Landau-Fermi-Dirac equation with Coulomb
potential. The initial conditions are nonnegative, bounded and integrable. We
also show that any weak solution converges towards the steady state given by
the Fermi-Dirac statistics. Furthermore, the convergence is algebraic, provided
that the initial datum is close to the steady state in a suitable weighted
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solutions to the homogeneous Landau-Fermi-Dirac equation with Coulomb
potential. The initial conditions are nonnegative, bounded and integrable. We
also show that any weak solution converges towards the steady state given by
the Fermi-Dirac statistics. Furthermore, the convergence is algebraic, provided
that the initial datum is close to the steady state in a suitable weighted
Lebesgue norm.</abstract><doi>10.48550/arxiv.2107.10463</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Analysis of PDEs |
| title | Existence of smooth solutions to the Landau-Fermi-Dirac equation with Coulomb potential |
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