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arxiv: 2509.20505 · v2 · submitted 2025-09-24 · 🧮 math.AP

Increased lifespan for 3D compressible Euler flows with rotation

Haram Ko , Benoit Pausader , Ryo Takada , Klaus Widmayer This is my paper

Pith reviewed 2026-05-18 13:30 UTC · model grok-4.3

classification 🧮 math.AP
keywords compressible EulerCoriolis termlifespan estimatesdispersive decayrotationincompressible limit
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The pith

Rotation increases the existence time for solutions of the compressible Euler equations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes a lower bound on the time of existence for solutions to the three-dimensional compressible Euler equations that include a Coriolis term. This bound depends explicitly on the rotation speed, the sound speed, and the size of the initial data. The authors derive the bound by obtaining precise dispersive decay estimates for the linearized system and using them to close a bootstrap argument. The same estimates improve known lifespan results in the incompressible limit. A reader would care because the result quantifies how rotation can delay or prevent finite-time breakdown in rotating fluid flows.

Core claim

For the compressible Euler equations with Coriolis force, the authors prove a lower bound on the lifespan of solutions that grows with the rotation speed and sound speed and shrinks with the size of the initial data. They obtain this by combining local existence theory with dispersive decay estimates for the linearized problem that capture the spreading induced by rotation.

What carries the argument

Dispersive decay estimates for the linearized compressible Euler-Coriolis system that yield improved decay rates proportional to the rotation speed and enable an extended bootstrap interval for the nonlinear solution.

If this is right

  • Solutions to rapidly rotating compressible Euler flows exist on longer time intervals.
  • The incompressible Euler-Coriolis system inherits an improved lifespan bound in the zero-sound-speed limit.
  • Rotation provides quantitative suppression of singularity formation in three-dimensional Euler flows.
  • Global existence becomes possible for sufficiently large rotation speeds or sufficiently small data.
  • The estimates supply a concrete rate at which rotation stabilizes the flow against breakdown.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The dependence on rotation speed might become sharp in certain scaling regimes, marking a transition to global existence.
  • The dispersive estimates could extend to related systems such as Euler equations with stratification or magnetic fields.
  • Numerical tests of the lifespan bound for concrete initial data would check the predicted scaling with rotation speed.
  • The result points toward studying how the incompressible limit interacts with the rotation-dependent dispersion.

Load-bearing premise

The initial data must be small enough in a suitable norm and regular enough for the local existence theory and the dispersive estimates to close the argument.

What would settle it

An explicit solution or numerical computation that develops a singularity strictly before the time predicted by the lower bound for given values of rotation speed, sound speed, and initial data size.

read the original abstract

We consider the compressible Euler equation with a Coriolis term and prove a lower bound on the time of existence of solutions in terms of the speed of rotation, sound speed and size of the initial data. Along the way, we obtain precise dispersive decay estimates for the linearized equation. In the incompressible limit, this improves current bounds for the incompressible Euler-Coriolis system as well.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript proves a lower bound on the existence time for solutions to the three-dimensional compressible Euler equations with Coriolis force. The bound is stated in terms of the rotation speed, sound speed, and initial data size. The argument proceeds by establishing precise dispersive decay estimates for the linearized compressible Euler-Coriolis system and closing a bootstrap argument for the nonlinear problem. In the incompressible limit the result improves existing lifespan bounds for the incompressible Euler-Coriolis system.

Significance. If the central estimates hold, the work supplies rotation-dependent lifespan lower bounds for compressible rotating fluids, a setting relevant to geophysical fluid dynamics. The linear dispersive decay estimates are of independent technical value and the improvement in the incompressible limit addresses a concrete gap in prior analyses of the Euler-Coriolis system.

minor comments (2)
  1. The dependence of the lifespan lower bound on the sound speed and rotation rate should be stated explicitly in the main theorem statement rather than only in the abstract.
  2. Notation for the Coriolis parameter and the sound speed is introduced without a dedicated preliminary section; a short notation table or paragraph would improve readability.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive and constructive report, including the recognition of the technical value of the linear dispersive decay estimates and the improvement over existing incompressible Euler-Coriolis lifespan bounds. We appreciate the recommendation for minor revision.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained via standard estimates

full rationale

The paper establishes a rotation-dependent lower bound on solution lifespan for the compressible Euler-Coriolis system by deriving precise dispersive decay estimates for the linearized problem and closing a perturbative bootstrap argument around local existence. These steps rely on classical linear dispersive analysis and small-data perturbative nonlinear estimates that are independent of the final lifespan scaling; the bound is obtained as an output of the estimates rather than being presupposed or fitted into the inputs. No self-definitional reductions, fitted parameters renamed as predictions, or load-bearing self-citations appear in the described chain. The argument is externally falsifiable through the explicit dependence on rotation speed, sound speed, and initial data size.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based on abstract only; no free parameters, invented entities, or non-standard axioms are mentioned. The result relies on standard local well-posedness theory for compressible Euler and dispersive estimates for the linear Coriolis operator.

axioms (1)
  • domain assumption Standard local existence and continuation criteria for smooth solutions of compressible Euler equations hold under the given initial data assumptions.
    Implicit in any lifespan lower-bound proof for quasilinear hyperbolic systems.

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Reference graph

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