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arXiv · 2601.16053

Fujita exponents on quantum Euclidean spaces

Edward McDonald·Michael Ruzhansky·Serikbol Shaimardan·Kanat Tulenov
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Abstract

We study the well-posedness of a non-linear heat equation with power nonlinearity with positive initial data on quantum Euclidean spaces. We prove a noncommutative analogue of the classical Fujita theorem by identifying the critical exponent separating finite-time blow-up from global existence for small initial data. Moreover, we establish a fundamental inequality in general semifinite von Neumann algebras that is of independent interest and plays a crucial role in the study of global existence and local well-posedness of solutions of nonlinear equations in noncommutative setting.

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Edward McDonald, Michael Ruzhansky, Serikbol Shaimardan, Kanat Tulenov. 2026-01-22. Fujita exponents on quantum Euclidean spaces. https://arxiv.org/abs/2601.16053

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