Establishes optimal local well-posedness for reaction-diffusion SPDEs with non-trace-class multiplicative noise, critical initial-data spaces, instantaneous regularization, and applications to prototypical models.
Grafakos,Classical Fourier analysis, 3rd ed., Graduate Texts in Mathematics, vol
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Introduces the complex mZK equation on T² and proves local well-posedness in Sobolev spaces together with failure of uniform continuity of the data-to-solution map.
Spectral asymptotics for negative fractional powers of hypoelliptic operators on graded Lie groups generalize Birman-Solomyak and imply a version of Connes' integration formula.
A pseudospectral multishape method is developed to accurately approximate singular convolution operators in the nonlocal Cahn-Hilliard equation, enabling efficient high-resolution phase separation simulations.
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An optimal local theory for reaction-diffusion equations driven by non-trace-class noise
Establishes optimal local well-posedness for reaction-diffusion SPDEs with non-trace-class multiplicative noise, critical initial-data spaces, instantaneous regularization, and applications to prototypical models.
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Complex-valued modified Zakharov Kuznetsov equation
Introduces the complex mZK equation on T² and proves local well-posedness in Sobolev spaces together with failure of uniform continuity of the data-to-solution map.