Stochastic Korteweg-de Vries equation driven by fractional Brownian motion

Wang, Guolian; Guo, Boling

doi:10.3934/dcds.2015.35.5255

Search citation statements

Order By: Relevance

Paper Sections

Select...

Stochastic High-order Degasperis-procesi Equation2

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2019

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(2 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Using Bourgain space and bilinear estimates, the regularity of Z(t) with H ∈ [7/16, 1) has been proved in [37]. But it needs φ is a Hilbert-Schmidt operator.…”

Section: Stochastic High-order Degasperis-procesi Equationmentioning

confidence: 99%

See 1 more Smart Citation

Periodic stochastic high-order Degasperis–Procesi equation with cylindrical fBm

2019

View full text Add to dashboard Cite

This paper studies the periodic stochastic high-order Degasperis–Procesi (DP) equation driven by a cylindrical fractional Brownian motion (fBm) which is white in space. And it has the covariance with Hurst parameter [Formula: see text] in the time variable. The local existence and uniqueness of the solution [Formula: see text] in [Formula: see text] with [Formula: see text] are proved by fixed point theorem combined with the stochastic term estimations in the Besov-type Bourgain space [Formula: see text] and the second iteration of non-linear term.

show abstract

“…Using Bourgain space and bilinear estimates, the regularity of Z(t) with H ∈ [7/16, 1) has been proved in [37]. But it needs φ is a Hilbert-Schmidt operator.…”

Section: Stochastic High-order Degasperis-procesi Equationmentioning

confidence: 99%

“…While H = 1 2 , the result in [34] is included in Theorem 1.2. Compared with the result in [37], φ is the identity operator here.…”

Section: Stochastic High-order Degasperis-procesi Equationmentioning

confidence: 99%