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• W4366998504 abstract "We study the swarming behavior of hydrodynamic alignment. Alignment reflects steering toward a weighted average heading. We consider the class of so-called <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=p> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=application/x-tex>p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-alignment hydrodynamics, based on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=2 p> <mml:semantics> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>p</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>2p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-Laplacians and weighted by a general family of symmetric communication kernels. The main new aspect here is the long-time emergence behavior for a general class of pressure tensors <italic>without</italic> a closure assumption, beyond the mere requirement that they form an energy dissipative process. We refer to such pressure laws as “entropic”, and prove the flocking of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=p> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=application/x-tex>p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-alignment hydrodynamics, driven by singular kernels with a general class of entropic pressure tensors. These results indicate the rigidity of alignment in driving long-time flocking behavior despite the lack of thermodynamic closure." @default.
• W4366998504 created "2023-04-27" @default.
• W4366998504 creator A5072355478 @default.
• W4366998504 date "2023-04-25" @default.
• W4366998504 modified "2023-10-18" @default.
• W4366998504 title "Swarming: hydrodynamic alignment with pressure" @default.
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• W4366998504 doi "https://doi.org/10.1090/bull/1793" @default.
• W4366998504 hasPublicationYear "2023" @default.
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