On the stochastic Korteweg-de Vries equation
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Publication:1270228
DOI10.1006/jfan.1997.3184zbMath0912.60074OpenAlexW2045776586MaRDI QIDQ1270228
Arnaud Debussche, Anne de Bouard
Publication date: 18 May 1999
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jfan.1997.3184
Korteweg-de Vries equationexistence and uniquenessstochastic partial differential equationmultiplicative noise
KdV equations (Korteweg-de Vries equations) (35Q53) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)
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Cites Work
- Unnamed Item
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- Unnamed Item
- On the Korteweg-de Vries equation
- Calderón-Zygmund theory for operator-valued kernels
- Remarks on the Korteweg-de Vries equation
- Solutions of the Korteweg-de Vries equation in fractional order Sobolev spaces
- Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
- The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices
- Martingale and stationary solutions for stochastic Navier-Stokes equations
- Sur un problème non linéaire
- Sur un théorème d'interpolation
- On the excitation of long nonlinear water waves by a moving pressure distribution
- Generation of upstream advancing solitons by moving disturbances
- Interpolation between $H^{1}_{B_{0}}$ and $L^{P}_{B_{1}}$
- Well-Posedness of the Initial Value Problem for the Korteweg-de Vries Equation
- The initial-value problem for the Korteweg-de Vries equation
- THE CAUCHY PROBLEM FOR A THIRD ORDER NONLINEAR SCHRÖDINGER EQUATION
- Korteweg-de Vries Equation and Generalizations. IV. The Korteweg-de Vries Equation as a Hamiltonian System
- A bilinear estimate with applications to the KdV equation
- The initial-value problem for the forced Korteweg-de Vries equation
- Stochastic Equations in Infinite Dimensions