Paclitaxel and Celecoxib in Treating Patients With Recurrent or Persistent Platinum-Resistant Ovarian Epithelial or Primary Peritoneal Cancer

DISEASE CHARACTERISTICS: * Histologically confirmed ovarian epithelial or primary peritoneal cancer * Recurrent or persistent disease * Measurable disease * At least 1 unidimensionally measurable lesion at least 20 mm by conventional techniques OR at least 10 mm by spiral CT scan * At least 1 target lesion not in a previously irradiated field * Must have received 1 prior platinum-based chemotherapy regimen for primary disease containing carboplatin, cisplatin, or another organoplatinum compound * Initial treatment may have included high-dose therapy, consolidation, or extended therapy administered after surgical or non-surgical assessment * Platinum-resistant or refractory (i.e., had a treatment-free interval after platinum therapy of less than 6 months OR disease progression during platinum-based therapy) * Patients who have not received a prior taxane may have received a second regimen that included paclitaxel or docetaxel * Must not be eligible for a higher priority GOG protocol PATIENT CHARACTERISTICS: Age * Not specified Performance status * GOG 0-2 Life expectancy * Not specified Hematopoietic * Absolute neutrophil count ≥ 1,500/mm\^3 * Platelet count ≥ 100,000/mm\^3 Hepatic * SGOT ≤ 2.5 times upper limit of normal (ULN) * Alkaline phosphatase ≤ 2.5 times ULN * Bilirubin ≤ 1.5 times ULN Renal * Creatinine ≤ 1.5 times ULN Other * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No active infection requiring antibiotics * No neuropathy (sensory and motor) \> grade 1 * No history of peptic ulcer disease * No allergies to sulfa or non-steroidal anti-inflammatory drugs * No known hypersensitivity to paclitaxel or celecoxib * No other invasive malignancy within the past 5 years except non-melanoma skin cancer PRIOR CONCURRENT THERAPY: Biologic therapy * At least 3 weeks since prior biologic or immunologic therapy * One prior non-cytotoxic\* regimen for recurrent or persistent disease allowed NOTE: \*Non-cytotoxic (biologic or cytostatic) agents include (but are not limited to) monoclonal antibodies, cytokines, and small-molecule inhibitors of signal transduction Chemotherapy * See Disease Characteristics * Recovered from prior chemotherapy * No other prior cytotoxic chemotherapy for recurrent or persistent disease, including retreatment with initial chemotherapy regimen Endocrine therapy * At least 1 week since prior hormonal therapy for malignant tumor * Concurrent hormone replacement therapy allowed Radiotherapy * See Disease Characteristics * Recovered from prior radiotherapy * No prior radiotherapy to more than 25% of marrow-bearing areas Surgery * See Disease Characteristics * Recovered from prior surgery Other * At least 3 weeks since prior therapy for malignant tumor * No prior celecoxib * No prior therapy for a previous cancer that would preclude protocol therapy * No concurrent amifostine or other protective agents