| Citation: |
Zishuo Chen, Qingning Zhang. LOCAL WELL-POSEDNESS IN CRITICAL BESOV SPACES, BLOW-UP ANALYSIS, AND GLOBAL EXISTENCE OF SOLUTIONS FOR THE B-FAMILY FOKAS-OLVER-ROSENAU-QIAO EQUATIONS[J]. Journal of Applied Analysis & Computation, 2026, 16(6): 2981-3002. doi: 10.11948/20250285
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LOCAL WELL-POSEDNESS IN CRITICAL BESOV SPACES, BLOW-UP ANALYSIS, AND GLOBAL EXISTENCE OF SOLUTIONS FOR THE B-FAMILY FOKAS-OLVER-ROSENAU-QIAO EQUATIONS
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Abstract
This work establishes the local well-posedness of the $b$-family Fokas-Olver-Rosenau-Qiao (bFORQ) equations in the critical Besov space $B_{2, 1}^{5/2}(\mathbb{R})$. We then analyze two special cases: For $b=1$, we prove finite-time blow-up of solutions with the explicit blow-up time $T^* \leq - 1/\left(\epsilon u_{0x}(x_1)m_0(x_1)\right)$; for $b=0$, we show the existence of global solutions in time.
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References
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Zishuo Chen, Qingning Zhang. LOCAL WELL-POSEDNESS IN CRITICAL BESOV SPACES, BLOW-UP ANALYSIS, AND GLOBAL EXISTENCE OF SOLUTIONS FOR THE B-FAMILY FOKAS-OLVER-ROSENAU-QIAO EQUATIONS[J]. Journal of Applied Analysis & Computation, 2026, 16(6): 2981-3002. doi: 10.11948/20250285
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