Critical exponent of Fujita type for semilinear wave equations in Friedmann–Lemaître–Robertson–Walker spacetime

Ebert, Marcelo Rempel; Marques, Jorge

doi:10.1002/mma.8663

Math Methods in App Sciences

2022

DOI: 10.1002/mma.8663

|View full text |Cite

Critical exponent of Fujita type for semilinear wave equations in Friedmann–Lemaître–Robertson–Walker spacetime

Marcelo Rempel Ebert

Jorge Marques

Abstract: We consider the nonlinear massless wave equation belonging to some family of the Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime. We prove the global in time small data solutions for supercritical powers in the case of decelerating expansion universe.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Global existence and blowup of smooth solutions to the semilinear wave equations in FLRW spacetime

Wei,

Yong

2024

Journal of Mathematical Physics

View full text Add to dashboard Cite

We are interested in the semilinear wave equations evolving in the expanding spacetimes with Friedmann–Lemaître–Robertson–Walker (FLRW) metric. By the weighted energy estimate, we show that when the nonlinearity depends on the time derivative of the unknown, the equation admits a global smooth solution if the spacetime is undergoing accelerated expansion. While the solution will blowup in the sense of some averaged quantity if the expanding rate is not fast enough. When the nonlinearity depends on the space derivatives of the unknown or the unknown itself, we can show that the solution will blowup in finite time even though the expanding rate is fast enough (accelerated expansion). Our results show that the semilinear wave equations in FLRW spacetimes have different properties from the famous Glassey and Strauss conjectures in flat or asymptotically flat spacetimes.

show abstract

Global existence and blowup of smooth solutions to the semilinear wave equations in FLRW spacetime

Wei,

Yong

2024

Journal of Mathematical Physics

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

hi@scite.ai

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Critical exponent of Fujita type for semilinear wave equations in Friedmann–Lemaître–Robertson–Walker spacetime

Abstract: We consider the nonlinear massless wave equation belonging to some family of the Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime. We prove the global in time small data solutions for supercritical powers in the case of decelerating expansion universe.

Cited by 1 publication

References 28 publications

Global existence and blowup of smooth solutions to the semilinear wave equations in FLRW spacetime

Global existence and blowup of smooth solutions to the semilinear wave equations in FLRW spacetime

Contact Info

Product

Resources

About