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.
From: Edward McDonald [view email]
[v1]
Thu, 22 Jan 2026 15:36:02 UTC (30 KB)
[v2]
Tue, 2 Jun 2026 09:40:20 UTC (30 KB)
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