The blow-up solutions for fractional heat equations on torus and Euclidean space

Bhimani, Divyang G.

doi:10.1007/s00030-022-00828-6

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“…Lemma 2.1 (Basic properties in p w p,q , see e.g. Lemma 2.1 in [5], [25]). Let p j , q j , p, q P r1, 8s and s i , s P R, where j " 1, 2.…”

Section: Key Estimatesmentioning

confidence: 99%

Norm Inflation for Benjamin–Bona–Mahony Equation in Fourier Amalgam and Wiener Amalgam Spaces with Negative Regularity

Bhimani

Haque

2021

Mathematics

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We consider the Benjamin–Bona–Mahony (BBM) equation of the form ut+ux+uux−uxxt=0,(x,t)∈M×R where M=T or R. We establish norm inflation (NI) with infinite loss of regularity at general initial data in Fourier amalgam and Wiener amalgam spaces with negative regularity. This strengthens several known NI results at zero initial data in Hs(T) established by Bona–Dai (2017) and the ill-posedness result established by Bona–Tzvetkov (2008) and Panthee (2011) in Hs(R). Our result is sharp with respect to the local well-posedness result of Banquet–Villamizar–Roa (2021) in modulation spaces Ms2,1(R) for s≥0.

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“…Lemma 2.1 (Basic properties in p w p,q , see e.g. Lemma 2.1 in [5], [25]). Let p j , q j , p, q P r1, 8s and s i , s P R, where j " 1, 2.…”

Section: Key Estimatesmentioning

confidence: 99%

Norm Inflation for Benjamin–Bona–Mahony Equation in Fourier Amalgam and Wiener Amalgam Spaces with Negative Regularity

Bhimani

Haque

2021

Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

The blow-up solutions for fractional heat equations on torus and Euclidean space

Cited by 1 publication

References 14 publications

Norm Inflation for Benjamin–Bona–Mahony Equation in Fourier Amalgam and Wiener Amalgam Spaces with Negative Regularity

Norm Inflation for Benjamin–Bona–Mahony Equation in Fourier Amalgam and Wiener Amalgam Spaces with Negative Regularity

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