| Abstract: |
| Well-posedness of stochastic Degasperis-Procesi equation
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Nikolai V. Chemetov (DCM - FFCLRP, University of Sao Paulo, Brazil)
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This talk is concerned with the existence of a solution to the stochastic
Degasperis-Procesi equation on R with an infinite dimensional multiplicative
noise and integrable initial data.
Writing the equation as a system composed of a stochastic nonlinear
conservation law and an elliptic equation [1], we are able to develop a
method based on the conjugation of kinetic theory [2] with stochastic
compactness arguments. More precisely, we apply the stochastic
Jakubowski-Skorokhod representation theorem to show the existence of a weak
kinetic martingale solution [3].
We also demonstrate the uniqueness result [4].
This is a joint work with Fernanda Cipriano (Universidade Nova de Lisboa,
Portugal).
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Bibliography:
1. L.K. Arruda, N.V. Chemetov, F. Cipriano, Solvability of the Stochastic
Degasperis-Procesi Equation. J. Dynamics and Differential Equations, 35(1)
(2023), 523-542.
2. N.V. Chemetov, W Neves, The generalized Buckley--Leverett system:
solvability. Archive for Rational Mechanics and Analysis, 208 (1) (2013),
1-24.
3. N.V. Chemetov, F. Cipriano, Weak solution for stochastic
Degasperis-Procesi equation. J. Differential Equations, Vol. 382 (15)
(2024), 1-49.
4. N.V. Chemetov, F. Cipriano, The uniqueness result for the weak solution
for stochastic Degasperis-Procesi equation. To be submitted. |
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