Delayed blow-up by transport noise
Franco Flandoli, Lucio Galeati, Dejun Luo
Abstract
For some deterministic nonlinear PDEs on the torus whose solutions may blow up in finite time, we show that, under suitable conditions on the nonlinear term, the blow-up is delayed by multiplicative noise of transport type in a certain scaling limit. The main result is applied to the 3D Keller–Segel, 3D Fisher–KPP, and 2D Kuramoto–Sivashinsky equations, yielding long-time existence for large initial data with high probability.
Topics & Concepts
MathematicsMultiplicative noiseTorusNoise (video)Nonlinear systemMultiplicative functionScalingLimit (mathematics)Term (time)Scaling limitMathematical analysisApplied mathematicsType (biology)Initial value problemStatistical physicsGeometryPhysicsComputer scienceSignal transfer functionBiologyAnalog signalDigital signal processingQuantum mechanicsEcologyComputer hardwareArtificial intelligenceImage (mathematics)Mathematical Biology Tumor GrowthStochastic processes and financial applicationsAdvanced Mathematical Modeling in Engineering