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Award ID contains: 2204614

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  1. ; ; (, Communications on Pure and Applied Mathematics)
    Abstract We prove the existence and uniqueness of global smooth solutions of the critical dissipative SQG equation in bounded domains in . We introduce a new methodology of transforming the single nonlocal nonlinear evolution equation in a bounded domain into an interacting system of extended nonlocal nonlinear evolution equations in the whole space. The proof then uses the method of the nonlinear maximum principle for nonlocal operators in the extended system. 
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    Free, publicly-accessible full text available January 1, 2026
  2. ; ; (, Nonlinear Differential Equations and Applications NoDEA)
    Abstract We consider a stochastic electroconvection model describing the nonlinear evolution of a surface charge density in a two-dimensional fluid with additive stochastic forcing. We prove the existence and uniqueness of solutions, we define the corresponding Markov semigroup, and we study its Feller properties. When the noise forces enough modes in phase space, we obtain the uniqueness of the smooth invariant measure for the Markov transition kernels associated with the model. 
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  3. ; (, Journal of Evolution Equations)
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  4. (, Journal of Mathematical Fluid Mechanics)
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  5. ; (, Journal of Differential Equations)
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  6. ; (, Indiana University Mathematics Journal)
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  7. ; ; (, Physica D: Nonlinear Phenomena)
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  8. ; (, Journal of Mathematical Fluid Mechanics)
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