Remark on Asymptotic Order for the Energy Critical Nonlinear Damped Wave Equation to the Linear Heat Equation via the Strichartz Estimates

Inui, Takahisa

doi:10.1007/978-3-030-58215-9_10

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Tx1

Proposition 1 (Homogeneous Strichartz Estimates)1

Remark 4 (Comparison With Damped Klein-gordon Equations)1

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2021

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(3 citation statements)

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“…-norm. Roughly speaking, the solutions behave like those of the linear heat equation (see [6] and Remark 4 below).…”

Section: Txmentioning

confidence: 94%

“…(Sketch of the proofs of the endpoint Strichartz estimate) First, we divide the solution map into the low-and high-frequency parts. Since the low-frequency part behaves like heat propagator, we have the endpoint estimate for the low frequency part (see [6,Lemma 2.3]). Thus, it is enough to treat the high frequency.…”

Section: Proposition 1 (Homogeneous Strichartz Estimates)mentioning

confidence: 99%

“…They are useful to investigate heat-like properties of the damped wave equation. Indeed, in [6], we have the following asymptotic result of (NLDW) by using them:…”

Section: Remark 4 (Comparison With Damped Klein-gordon Equations)mentioning

confidence: 99%

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Unconditional well-posedness for the energy-critical nonlinear damped wave equation

Inui

Wakasugi

2021

J. Evol. Equ.

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For the energy-critical nonlinear damped wave equation, we show the unconditional wellposedness. The unconditional well-posedness means local well-posedness and the unconditional uniqueness. First, we give the local well-posedness and stability, whose statement will be useful to investigate the global dynamics. At second, we show the unconditional uniqueness. Since these problems seem not to be solvable as a direct perturbation of the wave equation, we apply the Strichartz estimates for the damped wave equation including the wave endpoint case. 4 d−2 w.(NLW)These equations are invariant under the scaling:2 w(λt, λx),

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“…-norm. Roughly speaking, the solutions behave like those of the linear heat equation (see [6] and Remark 4 below).…”

Section: Txmentioning

confidence: 94%

Section: Proposition 1 (Homogeneous Strichartz Estimates)mentioning

confidence: 99%

See 1 more Smart Citation

Unconditional well-posedness for the energy-critical nonlinear damped wave equation

Inui

Wakasugi

2021

J. Evol. Equ.

Self Cite

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show abstract

Remark on Asymptotic Order for the Energy Critical Nonlinear Damped Wave Equation to the Linear Heat Equation via the Strichartz Estimates

Cited by 1 publication

References 7 publications

Unconditional well-posedness for the energy-critical nonlinear damped wave equation

Unconditional well-posedness for the energy-critical nonlinear damped wave equation

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