##  [Finite-Time Blow-Up](/finite-time-blow) 

  ##  [Finite-Time Blow-Up](https://mathlogic.quantumdictionary.io/finite-time-blow-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A failure mode in which a solution norm or a field quantity becomes unbounded in finite time, meaning that certain norms of the solution diverge as time approaches a finite blow-up time and classical solution existence breaks down.

 

 

 

 

 





 

 



 ##  [Finite-Time Blow-Up](https://puremath.quantumdictionary.io/finite-time-blow-1) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A dynamical failure mode in which a solution's norm or a related observable becomes unbounded in finite time, indicating breakdown of classical continuation and loss of regularity.