Global Well-Posedness for Aggregation Equation with Time-Space Nonlocal Operator and Shear Flow

Binbin Shi; Weike Wang

doi:10.1007/s42967-022-00214-0

Communications on Applied Mathematics and Computation ›› 2022, Vol. 5 ›› Issue (3) : 1274-1288. DOI: 10.1007/s42967-022-00214-0

Original Paper

Global Well-Posedness for Aggregation Equation with Time-Space Nonlocal Operator and Shear Flow

Binbin Shi¹ ,
Weike Wang²^,b

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Abstract

In this paper, we consider the two-dimensional aggregation equation with the shear flow and time-space nonlocal attractive operator. Without the advection, the solution of the aggregation equation may blow up in finite time. We show that the shear flow can suppress the blow-up.

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Binbin Shi, Weike Wang. Global Well-Posedness for Aggregation Equation with Time-Space Nonlocal Operator and Shear Flow. Communications on Applied Mathematics and Computation, 2022, 5(3): 1274‒1288 https://doi.org/10.1007/s42967-022-00214-0

Funding

Science and Technology Innovation Plan Of Shanghai Science and Technology Commission(21JC1403600); National Natural Science Foundation of China(11831011)