Presented By: Department of Mathematics
Differential Equations Seminar
Quasiperiodic solutions and inviscid limit for Euler and Navier Stokes equations via KAM methods
In this talk I will discuss some recent results on Euler and Navier Stokes equations concerning the construction of quasiperiodic solutions and the problem of the invscid limit for the Navier Stokes equation. I will discuss the following two results:
1) Construction of quasiperiodic solutions for the Euler equation with a time quasiperiodic external force, bifurcating from a constant, diophantine velocity field
2) I shall discuss the inviscid limit problem from the perspective of KAM theory, namely I shall prove the existence of quasiperiodic solutions of the Navier Stokes equation converging to the one of the Euler equation constructed in 1).
The main difficulty is that this is a singular limit problem. We overcome this difficulty by implementing a normal form methods which allow to prove sharp estimates (global in time) with respect to the viscosity parameter. Speaker(s): Riccardo Montalto (University of Milan)
1) Construction of quasiperiodic solutions for the Euler equation with a time quasiperiodic external force, bifurcating from a constant, diophantine velocity field
2) I shall discuss the inviscid limit problem from the perspective of KAM theory, namely I shall prove the existence of quasiperiodic solutions of the Navier Stokes equation converging to the one of the Euler equation constructed in 1).
The main difficulty is that this is a singular limit problem. We overcome this difficulty by implementing a normal form methods which allow to prove sharp estimates (global in time) with respect to the viscosity parameter. Speaker(s): Riccardo Montalto (University of Milan)
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