Norm inflation for the Boussinesq system

Zongyuan LI; Weinan Wang

doi:10.3934/dcdsb.2020353

Norm inflation for the Boussinesq system

Zongyuan LI, Weinan Wang

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

6 Citations (Scopus)

Abstract

We prove the norm inflation phenomena for the Boussinesq system on T³ . For arbitrarily small initial data (u₀, ρ₀) in the negative-order Besov spaces B˙⁻¹_∞,∞ × B˙⁻¹_∞,∞, the solution can become arbitrarily large in a short time. Such largeness can be detected in ρ in Besov spaces of any negative order: B˙^−s_∞,∞ for any s > 0.

Original language	English
Pages (from-to)	5449–5463
Journal	Discrete and Continuous Dynamical Systems. Series B
Volume	26
Issue number	10
Online published	Nov 2020
DOIs	https://doi.org/10.3934/dcdsb.2020353
Publication status	Published - Oct 2021
Externally published	Yes

Research Keywords

Boussinesq system
norm inflation
ill-posedness
negative order Besov spaces
plane waves

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title = "Norm inflation for the Boussinesq system",

abstract = "We prove the norm inflation phenomena for the Boussinesq system on T3 . For arbitrarily small initial data (u0, ρ0) in the negative-order Besov spaces B˙−1∞,∞ × B˙−1∞,∞, the solution can become arbitrarily large in a short time. Such largeness can be detected in ρ in Besov spaces of any negative order: B˙−s∞,∞ for any s > 0.",

keywords = "Boussinesq system, norm inflation, ill-posedness, negative order Besov spaces, plane waves",

author = "Zongyuan LI and Weinan Wang",

year = "2021",

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doi = "10.3934/dcdsb.2020353",

language = "English",

volume = "26",

pages = "5449–5463",

journal = "Discrete and Continuous Dynamical Systems. Series B",

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T1 - Norm inflation for the Boussinesq system

AU - LI, Zongyuan

AU - Wang, Weinan

PY - 2021/10

Y1 - 2021/10

N2 - We prove the norm inflation phenomena for the Boussinesq system on T3 . For arbitrarily small initial data (u0, ρ0) in the negative-order Besov spaces B˙−1∞,∞ × B˙−1∞,∞, the solution can become arbitrarily large in a short time. Such largeness can be detected in ρ in Besov spaces of any negative order: B˙−s∞,∞ for any s > 0.

AB - We prove the norm inflation phenomena for the Boussinesq system on T3 . For arbitrarily small initial data (u0, ρ0) in the negative-order Besov spaces B˙−1∞,∞ × B˙−1∞,∞, the solution can become arbitrarily large in a short time. Such largeness can be detected in ρ in Besov spaces of any negative order: B˙−s∞,∞ for any s > 0.

KW - Boussinesq system

KW - norm inflation

KW - ill-posedness

KW - negative order Besov spaces

KW - plane waves

U2 - 10.3934/dcdsb.2020353

DO - 10.3934/dcdsb.2020353

M3 - RGC 21 - Publication in refereed journal

SN - 1531-3492

VL - 26

SP - 5449

EP - 5463

JO - Discrete and Continuous Dynamical Systems. Series B

JF - Discrete and Continuous Dynamical Systems. Series B

IS - 10

ER -

Norm inflation for the Boussinesq system

Abstract

Research Keywords

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