Journal
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
Volume 47, Issue 11, Pages 2217-2269Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/03605302.2022.2118608
Keywords
Existence analysis; fractional diffusion; interacting particle systems; mean-field limit; nonlocal porous-medium equation; propagation of chaos
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Funding
- Austrian Science Fund (FWF) [P30000, P33010, F65, W1245]
- Alexander von Humboldt Foundation
- European Research Council (ERC) under the European Union [101018153]
- European Research Council (ERC) [101018153] Funding Source: European Research Council (ERC)
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This paper performs a mean-field-type limit from stochastic moderately interacting many-particle systems with singular Riesz potential, resulting in nonlocal porous-medium equations in the whole space. The nonlocality is given by the inverse of a fractional Laplacian, and the limit equation can be interpreted as a transport equation with a fractional pressure. The paper also provides an existence analysis of the fractional porous-medium equation and concludes the propagation of chaos property.
A mean-field-type limit from stochastic moderately interacting many-particle systems with singular Riesz potential is performed, leading to nonlocal porous-medium equations in the whole space. The nonlocality is given by the inverse of a fractional Laplacian, and the limit equation can be interpreted as a transport equation with a fractional pressure. The proof is based on Oelschlager's approach and a priori estimates for the associated diffusion equations, coming from energy-type and entropy inequalities as well as parabolic regularity. An existence analysis of the fractional porous-medium equation is also provided, based on a careful regularization procedure, new variants of fractional Gagliardo-Nirenberg inequalities, and the div-curl lemma. A consequence of the mean-field limit estimates is the propagation of chaos property.
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