Electronic Research Archive

2020, Issue 4: 1529-1544. doi: 10.3934/era.2020080
Special Issues

Odd random attractors for stochastic non-autonomous Kuramoto-Sivashinsky equations without dissipation

• Received: 01 March 2020 Revised: 01 June 2020 Published: 31 July 2020
• Primary: 37L55; Secondary: 35B41, 60H15

• We study the random dynamics for the stochastic non-autonomous Kuramoto-Sivashinsky equation in the possibly non-dissipative case. We first prove the existence of a pullback attractor in the Lebesgue space of odd functions, then show that the fiber of the odd pullback attractor semi-converges to a nonempty compact set as the time-parameter goes to minus infinity and finally prove the measurability of the attractor. In a word, we obtain a longtime stable random attractor formed from odd functions. A key tool is the existence of a bridge function between Lebesgue and Sobolev spaces of odd functions.

Citation: Yangrong Li, Shuang Yang, Qiangheng Zhang. Odd random attractors for stochastic non-autonomous Kuramoto-Sivashinsky equations without dissipation[J]. Electronic Research Archive, 2020, 28(4): 1529-1544. doi: 10.3934/era.2020080

Related Papers:

• We study the random dynamics for the stochastic non-autonomous Kuramoto-Sivashinsky equation in the possibly non-dissipative case. We first prove the existence of a pullback attractor in the Lebesgue space of odd functions, then show that the fiber of the odd pullback attractor semi-converges to a nonempty compact set as the time-parameter goes to minus infinity and finally prove the measurability of the attractor. In a word, we obtain a longtime stable random attractor formed from odd functions. A key tool is the existence of a bridge function between Lebesgue and Sobolev spaces of odd functions.

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