A note on the blowup of scale invariant damping wave equation with sub-Strauss exponent

Abstract

We concern the blow up problem to the scale invariant damping wave equations with sub-Strauss exponent. This problem has been studied by Lai, Takamura and Wakasa (\cite{Lai17}) and Ikeda and Sobajima \cite{Ikedapre} recently. In present paper, we extend the blowup exponent from $p_F(n)\le p<p_S(n+2\mu )$ to $1<p<p_S(n+\mu )$ without small restriction on $\mu$. Moreover, the upper bound of lifespan is derived with uniform estimate $T(\epsilon )\le C{\epsilon }^{-2p(p-1)/\gamma (p,n+2\mu )}$. This result extends the blowup result of semilinear wave equation and shows the wave-like behavior of scale invariant damping wave equation's solution even with large $\mu >1$.

References in corpus (4)

• From $p_0(n)$ to $p_0(n+2)$
• Blow-up for semilinear wave equations with the scale invariant damping and super-Fujita exponent
• Blow-up for semilinear damped wave equations with sub-Strauss exponent in the scattering case
• Life-span of solutions to semilinear wave equation with time-dependent critical damping for specially localized initial data

Cited by in corpus (23)

• Fujita versus Strauss - a never ending story
• Lifespan of semilinear wave equation with scale invariant dissipation and mass and sub-Strauss power nonlinearity
• Nonexistence of global solutions of wave equations with weak time-dependent damping and combined nonlinearity
• Heat-like and wave-like lifespan estimates for solutions of semilinear damped wave equations via a Kato's type lemma
• Blow-up for a weakly coupled system of semilinear damped wave equations in the scattering case with power nonlinearities
• A note on a conjecture for the critical curve of a weakly coupled system of semilinear wave equations with scale-invariant lower order terms
• The lifespan of solutions of semilinear wave equations with the scale-invariant damping in two space dimensions
• Blow-up results for semilinear damped wave equations in Einstein-de Sitter spacetime
• Nonexistence of global solutions for generalized Tricomi equations with combined nonlinearity
• Weakly coupled system of semilinear wave equations with distinct scale-invariant terms in the linear part
• Wave-like blow-up for semilinear wave equations with scattering damping and negative mass term
• Lifespan estimates for the compressible Euler equations with damping via Orlicz spaces techniques
• Global well-posedness for the semilinear wave equation with time dependent damping in the overdamping case
• Integral representation formulae for the solution of a wave equation with time-dependent damping and mass in the scale-invariant case
• A competition on blow-up for semilinear wave equations with scale-invariant damping and nonlinear memory term
• Weighted $L^2-L^2$ estimate for wave equation and its applications
• Blow-up and lifespan estimates for a damped wave equation in the Einstein-de Sitter spacetime with nonlinearity of derivative type
• New blow-up result for the weakly coupled wave equations with a scale-invariant damping and time derivative nonlinearity
• Small data blow-up of semi-linear wave equation with scattering dissipation and time-dependent mass
• On the blow-up for critical semilinear wave equations with damping in the scattering case
• Short time blow-up by negative mass term for semilinear wave equations with small data and scattering damping
• Small data blow-up for the wave equation with a time-dependent scale invariant damping and a cubic convolution for slowly decaying initial data
• Critical exponent for the wave equation with a time-dependent scale invariant damping and a cubic convolution