SIAM Journal on Mathematical Analysis· 2026Q1
Blowup Solutions of the “Bad” Boussinesq Equation
- 0citations
- Q1SCImago
- 2026year
Short summary
This paper proves that the "bad" Boussinesq equation admits a wide range of blowup behaviors for its solutions, including wave-breaking scenarios where solutions remain bounded but their derivatives grow infinitely large in finite time.
AI-generated from the title and abstract; the full text is not read.
Key points
- The "bad" Boussinesq equation allows for a variety of asymptotic scenarios for its blowup solutions.
- Specific solutions are shown to approach distinct profiles as time tends to infinity.
- The existence of wave-breaking solutions is proven for particular parameter values.
- Wave-breaking solutions remain bounded while their derivatives blow up in finite time.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract. We study blowup solutions of the “bad” Boussinesq equation and prove that a wide range of asymptotic scenarios can happen. For example, for each [Formula: see text], [Formula: see text] and [Formula: see text], we prove that there exist Schwartz class solutions [Formula: see text] on [Formula: see text] such that [Formula: see text] and [Formula: see text] as [Formula: see text]. We also prove that for any [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], there exist Schwartz class solutions [Formula: see text] on [Formula: see text] such that [Formula: see text] for each [Formula: see text] such that [Formula: see text]; [Formula: see text] for each [Formula: see text] such that [Formula: see text]; and [Formula: see text] as [Formula: see text] for each [Formula: see text] such that [Formula: see text]. In particular, when [Formula: see text], this result establishes the existence of wave-breaking solutions, i.e., solutions that remain bounded but whose [Formula: see text]-derivative blows up in finite time.
The authors' abstract, as published at the source. SIAM Journal on Mathematical Analysis, 2026 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Mathematical Physics
Mathematical PhysicsMathematics