Fujita exponents on quantum Euclidean spaces
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915747748380672 |
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| author | McDonald, Edward Ruzhansky, Michael Shaimardan, Serikbol Tulenov, Kanat |
| author_facet | McDonald, Edward Ruzhansky, Michael Shaimardan, Serikbol Tulenov, Kanat |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16053 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fujita exponents on quantum Euclidean spaces McDonald, Edward Ruzhansky, Michael Shaimardan, Serikbol Tulenov, Kanat Analysis of PDEs Operator Algebras 42B37, 35G25, 46L52 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. |
| title | Fujita exponents on quantum Euclidean spaces |
| topic | Analysis of PDEs Operator Algebras 42B37, 35G25, 46L52 |
| url | https://arxiv.org/abs/2601.16053 |